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- La ecuación:
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Ecuación x+(x*3)=168
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Ecuación x^3+3*x^2=16*x+48
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Ecuación x*81=729/3
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Ecuación x^2=3x
- Expresar {x} en función de y en la ecuación:
- 6*x+4*y=15
- -4*x+4*y=-9
- 3*x-12*y=-14
- 10*x-9*y=-10
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Expresiones idénticas
- sesenta y cuatro *x^ cuatro + cuatro *x^ dos =a+ tres *x+(a+ tres *x)^ tres
- 64 multiplicar por x en el grado 4 más 4 multiplicar por x al cuadrado es igual a a más 3 multiplicar por x más (a más 3 multiplicar por x) al cubo
- sesenta y cuatro multiplicar por x en el grado cuatro más cuatro multiplicar por x en el grado dos es igual a a más tres multiplicar por x más (a más tres multiplicar por x) en el grado tres
- 64*x4+4*x2=a+3*x+(a+3*x)3
- 64*x4+4*x2=a+3*x+a+3*x3
- 64*x⁴+4*x²=a+3*x+(a+3*x)³
- 64*x en el grado 4+4*x en el grado 2=a+3*x+(a+3*x) en el grado 3
- 64x^4+4x^2=a+3x+(a+3x)^3
- 64x4+4x2=a+3x+(a+3x)3
- 64x4+4x2=a+3x+a+3x3
- 64x^4+4x^2=a+3x+a+3x^3
-
Expresiones semejantes
- 64*x^4-4*x^2=a+3*x+(a+3*x)^3
- 64*x^4+4*x^2=a+3*x-(a+3*x)^3
- 64*x^4+4*x^2=a-3*x+(a+3*x)^3
- 64*x^4+4*x^2=a+3*x+(a-3*x)^3
64*x^4+4*x^2=a+3*x+(a+3*x)^3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 2 3 64*x + 4*x = a + 3*x + (a + 3*x)
$$64 x^{4} + 4 x^{2} = \left(a + 3 x\right)^{3} + \left(a + 3 x\right)$$
Gráfica
Respuesta rápida
[src]
// __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ // __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \
|| / _____________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________ |
|| / / 2 | || / / 2 |
|| / / / 2\ 3 / 2 3\ 2 | || / / / 2\ 3 / 2 3\ 2 |
|| / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | || / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a |
|| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- | || / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- |
|| / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 | || / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 |
|| / ----- + 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- + ------------------------------------------------------------------------------------------------------------------------------------------------ | || / ----- + 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- + ------------------------------------------------------------------------------------------------------------------------------------------------ |
|| _______________________________________________________________________________________________________________________________________ / 24576 \/ 8 108 3 16 _______________________________________________________________________________________________________________________________________ | || _______________________________________________________________________________________________________________________________________ / 24576 \/ 8 108 3 16 _______________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________ |
|| / / 2 / / / 2 | || / / 2 / / / 2 |
|| / / / 2\ 3 / 2 3\ / / / / 2\ 3 / 2 3\ | || / / / 2\ 3 / 2 3\ / / / / 2\ 3 / 2 3\ |
|| / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2 | || / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2 |
|| / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 27*a\ | || / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 27*a\ |
|| / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- / / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- |- ----- - ----| 3 2 | || / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- / / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- |- ----- - ----| 3 2 |
|| 27 \/ 49152 \/ 8 108 3 32 \/ \/ 49152 \/ 8 108 3 32 19842003 \ 32768 64 / a 243*a 85219*a | || 27 \/ 49152 \/ 8 108 3 32 \/ \/ 49152 \/ 8 108 3 32 19842003 \ 32768 64 / a 243*a 85219*a |
|| --- - ------------------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for ---------- - ----------------- + -- + ------ + ------- = 0| || --- - ------------------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for ---------- - ----------------- + -- + ------ + ------- = 0|
|| 256 2 2 4294967296 12 64 16384 4194304 | || 256 2 2 4294967296 12 64 16384 4194304 |
|| | || |
|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
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|| / / / 2 | || / / / 2 |
|| / / / / 2 \ 3 | || / / / / 2 \ 3 |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ | || / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ 2 | |- ----- - ----| 3 2 | | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ 2 | |- ----- - ----| 3 2 | |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | 19842003 \ 32768 64 / a 243*a 85219*a| | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | 19842003 \ 32768 64 / a 243*a 85219*a| |
x1 = I*im|< / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- 2*|---------- - ----------------- + -- + ------ + -------| | + re|< / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- 2*|---------- - ----------------- + -- + ------ + -------| |
|| / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 \4294967296 12 64 16384 4194304/ | || / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 \4294967296 12 64 16384 4194304/ |
|| / ----- - 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / ----- - 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 24576 \/ \/ 4 27 16 216 6 16 _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 24576 \/ \/ 4 27 16 216 6 16 _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / ____________________________________________________________________________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ / / 2 | || / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / 2 \ 3 | || / / / 2 / / / / 2 / / / 2 \ 3 |
|| / / / / 2 \ 3 / / / / / 2 \ 3 / / | / 2\ 3 / 2 3\| / 2 \ | || / / / / 2 \ 3 / / / / / 2 \ 3 / / | / 2\ 3 / 2 3\| / 2 \ |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | || / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| |
|| / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ | || / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ |
|| / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ / / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- | || / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ / / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- |
|| / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- / / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 | || / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- / / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 |
|| / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ | || / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / 2 \ 3 / / / / / 2 \ 3 | || / / / / 2 \ 3 / / / / / 2 \ 3 |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ | || / / / | / 2\ 3 / 2 3\| / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| | || / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| |
|| / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ | || / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ |
|| / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- | || / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- |
|| 27 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 | || 27 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 |
||--- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||--- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
||256 2 2 | ||256 2 2 |
\\ / \\ /
$$x_{1} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}{2} - \frac{\sqrt{\frac{9 a}{16} + 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{24576} + \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}}}{2} + \frac{27}{256} & \text{for}\: \frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296} = 0 \\- \frac{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} - \frac{\sqrt{\frac{9 a}{16} + \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}} - 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{24576} + \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{27}{256} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}{2} - \frac{\sqrt{\frac{9 a}{16} + 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{24576} + \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}}}{2} + \frac{27}{256} & \text{for}\: \frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296} = 0 \\- \frac{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} - \frac{\sqrt{\frac{9 a}{16} + \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}} - 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{24576} + \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{27}{256} & \text{otherwise} \end{cases}\right)}$$
// __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ // __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \
|| / _____________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________ |
|| / / 2 | || / / 2 |
|| / / / 2\ 3 / 2 3\ 2 | || / / / 2\ 3 / 2 3\ 2 |
|| / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | || / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a |
|| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- | || / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- |
|| / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 | || / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 |
|| / ----- + 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- + ------------------------------------------------------------------------------------------------------------------------------------------------ | || / ----- + 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- + ------------------------------------------------------------------------------------------------------------------------------------------------ |
|| / 24576 \/ 8 108 3 16 _______________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________ | || / 24576 \/ 8 108 3 16 _______________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________ |
|| / / _____________________________________________________________________________________________________________ / _____________________________________________________________________________________________________________ | || / / _____________________________________________________________________________________________________________ / _____________________________________________________________________________________________________________ |
|| / / / 2 / / 2 | || / / / 2 / / 2 |
|| / / / / 2\ 3 / 2 3\ / / / 2\ 3 / 2 3\ | || / / / / 2\ 3 / 2 3\ / / / 2\ 3 / 2 3\ |
|| / / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2 | || / / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2 |
|| / / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 27*a\ | || / / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 27*a\ |
|| / / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- |- ----- - ----| 3 2 | || / / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- |- ----- - ----| 3 2 |
|| 27 \/ \/ 49152 \/ 8 108 3 32 \/ 49152 \/ 8 108 3 32 19842003 \ 32768 64 / a 243*a 85219*a | || 27 \/ \/ 49152 \/ 8 108 3 32 \/ 49152 \/ 8 108 3 32 19842003 \ 32768 64 / a 243*a 85219*a |
|| --- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------ for ---------- - ----------------- + -- + ------ + ------- = 0| || --- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------ for ---------- - ----------------- + -- + ------ + ------- = 0|
|| 256 2 2 4294967296 12 64 16384 4194304 | || 256 2 2 4294967296 12 64 16384 4194304 |
|| | || |
|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
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|| / / / 2 | || / / / 2 |
|| / / / / 2 \ 3 | || / / / / 2 \ 3 |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ | || / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ 2 | |- ----- - ----| 3 2 | | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ 2 | |- ----- - ----| 3 2 | |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | 19842003 \ 32768 64 / a 243*a 85219*a| | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | 19842003 \ 32768 64 / a 243*a 85219*a| |
x2 = I*im|< / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- 2*|---------- - ----------------- + -- + ------ + -------| | + re|< / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- 2*|---------- - ----------------- + -- + ------ + -------| |
|| / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 \4294967296 12 64 16384 4194304/ | || / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 \4294967296 12 64 16384 4194304/ |
|| / ----- - 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / ----- - 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| / 24576 \/ \/ 4 27 16 216 6 16 _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / 24576 \/ \/ 4 27 16 216 6 16 _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / ____________________________________________________________________________________________________________________________________________________________________________ / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / ____________________________________________________________________________________________________________________________________________________________________________ / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / / ____________________________________________________________________________________________________________________________________________________________________________ / / 2 / / ____________________________________________________________________________________________________________________________________________________________________________ | || / / / ____________________________________________________________________________________________________________________________________________________________________________ / / 2 / / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / / / 2 / / / 2 \ 3 / / / 2 | || / / / / 2 / / / 2 \ 3 / / / 2 |
|| / / / / / 2 \ 3 / / | / 2\ 3 / 2 3\| / 2 \ / / / / 2 \ 3 | || / / / / / 2 \ 3 / / | / 2\ 3 / 2 3\| / 2 \ / / / / 2 \ 3 |
|| / / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ | || / / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ |
|| / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | | || / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | |
|| / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | | || / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | |
|| / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| | || / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| |
|| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| | || / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| |
|| / / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ | || / / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ |
|| / / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| / / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / / ____________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________________________________________________________________ | || / / / ____________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / / / 2 / / / 2 | || / / / / 2 / / / 2 |
|| / / / / / 2 \ 3 / / / / 2 \ 3 | || / / / / / 2 \ 3 / / / / 2 \ 3 |
|| / / / / | / 2\ 3 / 2 3\| / 2 \ / / / | / 2\ 3 / 2 3\| / 2 \ | || / / / / | / 2\ 3 / 2 3\| / 2 \ / / / | / 2\ 3 / 2 3\| / 2 \ |
|| / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | || / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 |
|| / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | || / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ |
|| / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| | || / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| |
|| / / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ | || / / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ |
|| / / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- | || / / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- |
|| 27 \/ \/ \/ \/ 4 27 16 216 6 \/ \/ \/ 4 27 16 216 6 | || 27 \/ \/ \/ \/ 4 27 16 216 6 \/ \/ \/ 4 27 16 216 6 |
||--- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||--- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
||256 2 2 | ||256 2 2 |
\\ / \\ /
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}{2} + \frac{\sqrt{\frac{9 a}{16} + 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{24576} + \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}}}{2} + \frac{27}{256} & \text{for}\: \frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296} = 0 \\- \frac{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{\sqrt{\frac{9 a}{16} + \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}} - 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{24576} + \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{27}{256} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}{2} + \frac{\sqrt{\frac{9 a}{16} + 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{24576} + \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}}}{2} + \frac{27}{256} & \text{for}\: \frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296} = 0 \\- \frac{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{\sqrt{\frac{9 a}{16} + \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}} - 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{24576} + \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{27}{256} & \text{otherwise} \end{cases}\right)}$$
// __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ // __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \
|| / _____________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________ |
|| / / 2 | || / / 2 |
|| / / / 2\ 3 / 2 3\ 2 | || / / / 2\ 3 / 2 3\ 2 |
|| / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | || / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a |
|| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- | || / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- |
|| / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 | || / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 |
|| / ----- + 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------ | || / ----- + 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------ |
|| _______________________________________________________________________________________________________________________________________ / 24576 \/ 8 108 3 16 _______________________________________________________________________________________________________________________________________ | || _______________________________________________________________________________________________________________________________________ / 24576 \/ 8 108 3 16 _______________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________ |
|| / / 2 / / / 2 | || / / 2 / / / 2 |
|| / / / 2\ 3 / 2 3\ / / / / 2\ 3 / 2 3\ | || / / / 2\ 3 / 2 3\ / / / / 2\ 3 / 2 3\ |
|| / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2 | || / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2 |
|| / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 27*a\ | || / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 27*a\ |
|| / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- / / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- |- ----- - ----| 3 2 | || / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- / / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- |- ----- - ----| 3 2 |
|| 27 \/ 49152 \/ 8 108 3 32 \/ \/ 49152 \/ 8 108 3 32 19842003 \ 32768 64 / a 243*a 85219*a | || 27 \/ 49152 \/ 8 108 3 32 \/ \/ 49152 \/ 8 108 3 32 19842003 \ 32768 64 / a 243*a 85219*a |
|| --- + ------------------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for ---------- - ----------------- + -- + ------ + ------- = 0| || --- + ------------------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for ---------- - ----------------- + -- + ------ + ------- = 0|
|| 256 2 2 4294967296 12 64 16384 4194304 | || 256 2 2 4294967296 12 64 16384 4194304 |
|| | || |
|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / ____________________________________________________________________________________________________________________________________________________________________________ | || / / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / / 2 | || / / / 2 |
|| / / / / 2 \ 3 | || / / / / 2 \ 3 |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ | || / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ 2 | |- ----- - ----| 3 2 | | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ 2 | |- ----- - ----| 3 2 | |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | 19842003 \ 32768 64 / a 243*a 85219*a| | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | 19842003 \ 32768 64 / a 243*a 85219*a| |
x3 = I*im|< / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- 2*|---------- - ----------------- + -- + ------ + -------| | + re|< / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- 2*|---------- - ----------------- + -- + ------ + -------| |
|| / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 \4294967296 12 64 16384 4194304/ | || / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 \4294967296 12 64 16384 4194304/ |
|| / ----- - 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / ----- - 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 24576 \/ \/ 4 27 16 216 6 16 _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 24576 \/ \/ 4 27 16 216 6 16 _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
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|| / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ / / 2 | || / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / 2 \ 3 | || / / / 2 / / / / 2 / / / 2 \ 3 |
|| / / / / 2 \ 3 / / / / / 2 \ 3 / / | / 2\ 3 / 2 3\| / 2 \ | || / / / / 2 \ 3 / / / / / 2 \ 3 / / | / 2\ 3 / 2 3\| / 2 \ |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | || / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| |
|| / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ | || / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ |
|| / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ / / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- | || / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ / / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- |
|| / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- / / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 | || / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- / / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 |
|| / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ | || / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / 2 \ 3 / / / / / 2 \ 3 | || / / / / 2 \ 3 / / / / / 2 \ 3 |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ | || / / / | / 2\ 3 / 2 3\| / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| | || / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| |
|| / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ | || / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ |
|| / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- | || / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- |
|| 27 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 | || 27 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 |
||--- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||--- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
||256 2 2 | ||256 2 2 |
\\ / \\ /
$$x_{3} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}{2} - \frac{\sqrt{\frac{9 a}{16} + 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{24576} - \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}}}{2} + \frac{27}{256} & \text{for}\: \frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296} = 0 \\\frac{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} - \frac{\sqrt{\frac{9 a}{16} - \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}} - 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{24576} + \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{27}{256} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}{2} - \frac{\sqrt{\frac{9 a}{16} + 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{24576} - \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}}}{2} + \frac{27}{256} & \text{for}\: \frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296} = 0 \\\frac{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} - \frac{\sqrt{\frac{9 a}{16} - \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}} - 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{24576} + \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{27}{256} & \text{otherwise} \end{cases}\right)}$$
// __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ // __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \
|| / _____________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________ |
|| / / 2 | || / / 2 |
|| / / / 2\ 3 / 2 3\ 2 | || / / / 2\ 3 / 2 3\ 2 |
|| / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | || / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a |
|| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- | || / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- |
|| / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 | || / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 |
|| / ----- + 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------ | || / ----- + 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------ |
|| _______________________________________________________________________________________________________________________________________ / 24576 \/ 8 108 3 16 _______________________________________________________________________________________________________________________________________ | || _______________________________________________________________________________________________________________________________________ / 24576 \/ 8 108 3 16 _______________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________ |
|| / / 2 / / / 2 | || / / 2 / / / 2 |
|| / / / 2\ 3 / 2 3\ / / / / 2\ 3 / 2 3\ | || / / / 2\ 3 / 2 3\ / / / / 2\ 3 / 2 3\ |
|| / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2 | || / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2 |
|| / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 27*a\ | || / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / / 139 / \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a / 139 27*a\ |
|| / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- / / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- |- ----- - ----| 3 2 | || / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- / / ----- - 2*3 / - --------------------------- - ----------------- + ------------------------------------------------------- + --- |- ----- - ----| 3 2 |
|| 27 \/ 49152 \/ 8 108 3 32 \/ \/ 49152 \/ 8 108 3 32 19842003 \ 32768 64 / a 243*a 85219*a | || 27 \/ 49152 \/ 8 108 3 32 \/ \/ 49152 \/ 8 108 3 32 19842003 \ 32768 64 / a 243*a 85219*a |
|| --- + ------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for ---------- - ----------------- + -- + ------ + ------- = 0| || --- + ------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for ---------- - ----------------- + -- + ------ + ------- = 0|
|| 256 2 2 4294967296 12 64 16384 4194304 | || 256 2 2 4294967296 12 64 16384 4194304 |
|| | || |
|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / ____________________________________________________________________________________________________________________________________________________________________________ | || / / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / / 2 | || / / / 2 |
|| / / / / 2 \ 3 | || / / / / 2 \ 3 |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ | || / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ 2 | |- ----- - ----| 3 2 | | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ 2 | |- ----- - ----| 3 2 | |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | 19842003 \ 32768 64 / a 243*a 85219*a| | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | 90339 729*a 9*a | 19842003 \ 32768 64 / a 243*a 85219*a| |
x4 = I*im|< / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- 2*|---------- - ----------------- + -- + ------ + -------| | + re|< / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| - ------- - ----- - ---- 2*|---------- - ----------------- + -- + ------ + -------| |
|| / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 \4294967296 12 64 16384 4194304/ | || / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a 1048576 4096 32 \4294967296 12 64 16384 4194304/ |
|| / ----- - 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / ----- - 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 24576 \/ \/ 4 27 16 216 6 16 _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 24576 \/ \/ 4 27 16 216 6 16 _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / ____________________________________________________________________________________________________________________________________________________________________________ | || / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ / / 2 | || / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / 2 \ 3 | || / / / 2 / / / / 2 / / / 2 \ 3 |
|| / / / / 2 \ 3 / / / / / 2 \ 3 / / | / 2\ 3 / 2 3\| / 2 \ | || / / / / 2 \ 3 / / / / / 2 \ 3 / / | / 2\ 3 / 2 3\| / 2 \ |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | || / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ / 2 \ / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | / 139 27*a\ | / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | |- ----- - ----| 3 2 | / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | 19842003 \ 32768 64 / a 243*a 85219*a| / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| |
|| / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ | || / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| 2*|---------- - ----------------- + -- + ------ + -------| / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ |
|| / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ / / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- | || / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ / / 139 / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ 9*a \4294967296 12 64 16384 4194304/ 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- |
|| / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- / / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 | || / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- / / ----- + 2*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 |
|| / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / 49152 \/ \/ 4 27 16 216 6 32 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ | || / / ____________________________________________________________________________________________________________________________________________________________________________ / / / ____________________________________________________________________________________________________________________________________________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / 2 \ 3 / / / / / 2 \ 3 | || / / / / 2 \ 3 / / / / / 2 \ 3 |
|| / / / | / 2\ 3 / 2 3\| / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ | || / / / | / 2\ 3 / 2 3\| / 2 \ / / / / | / 2\ 3 / 2 3\| / 2 \ |
|| / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 | || / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 / / / / | | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a || | / 139 27*a\ | 2 |
|| / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ | || / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ / / / / | |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --|| | |- ----- - ----| 3 2 | / 2\ 3 / 2 3\ |
|| / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | | || / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | / / / / | \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/| | 19842003 \ 32768 64 / a 243*a 85219*a| | 90339 729*a 9*a | / 139 27*a\ / 139 27*a\ | 19842003 85219*a 243*a a | |
|| / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| | || / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| / / / / |- --------------------------- - ----------------- + -------------------------------------------------------| |---------- - ----------------- + -- + ------ + -------| |- ------- - ----- - ----| |- ----- - ----| |- ----- - ----|*|- ---------- - ------- - ------ - --| |
|| / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ | || / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ / / / / \ 8 108 3 / \4294967296 12 64 16384 4194304/ \ 2097152 8192 64 / \ 32768 64 / \ 32768 64 / \ 4294967296 4194304 16384 64/ |
|| / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- | || / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- / / 3*3 / / -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + --------------------------- + ----------------- - ------------------------------------------------------- |
|| 27 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 | || 27 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 |
||--- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||--- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
||256 2 2 | ||256 2 2 |
\\ / \\ /
$$x_{4} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}{2} + \frac{\sqrt{\frac{9 a}{16} + 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{24576} - \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}}}{2} + \frac{27}{256} & \text{for}\: \frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296} = 0 \\\frac{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{\sqrt{\frac{9 a}{16} - \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}} - 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{24576} + \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{27}{256} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}{2} + \frac{\sqrt{\frac{9 a}{16} + 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{24576} - \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} - 2 \sqrt[3]{- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}} + \frac{139}{49152}}}}}{2} + \frac{27}{256} & \text{for}\: \frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296} = 0 \\\frac{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{\sqrt{\frac{9 a}{16} - \frac{- \frac{9 a^{2}}{32} - \frac{729 a}{4096} - \frac{90339}{1048576}}{\sqrt{\frac{9 a}{32} + 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{49152} - \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}} - 2 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}} + \frac{139}{24576} + \frac{2 \left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)}{3 \sqrt[3]{\frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{216} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{6} + \sqrt{\frac{\left(- \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{3}}{108} + \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right) \left(- \frac{a^{3}}{64} - \frac{243 a^{2}}{16384} - \frac{85219 a}{4194304} - \frac{19842003}{4294967296}\right)}{3} - \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{8}\right)^{2}}{4} + \frac{\left(\frac{a^{3}}{64} + \frac{243 a^{2}}{16384} + \frac{85219 a}{4194304} - \frac{\left(- \frac{27 a}{64} - \frac{139}{32768}\right)^{2}}{12} + \frac{19842003}{4294967296}\right)^{3}}{27}} + \frac{\left(- \frac{9 a^{2}}{64} - \frac{729 a}{8192} - \frac{90339}{2097152}\right)^{2}}{16}}}}}{2} + \frac{27}{256} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((sqrt(9*a/32 - 2*(-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^(1/3) + 139/49152)/2 + sqrt(9*a/16 + 2*(-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^(1/3) + 139/24576 - (-9*a^2/32 - 729*a/4096 - 90339/1048576)/sqrt(9*a/32 - 2*(-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^(1/3) + 139/49152)/2 + 27/256, a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296 = 0), (sqrt(9*a/32 + 2*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3) + 139/49152 - 2*(a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)/(3*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3)))/2 + sqrt(9*a/16 - (-9*a^2/32 - 729*a/4096 - 90339/1048576)/sqrt(9*a/32 + 2*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3) + 139/49152 - 2*(a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)/(3*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3))) - 2*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3) + 139/24576 + 2*(a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)/(3*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3)))/2 + 27/256, True))) + i*im(Piecewise((sqrt(9*a/32 - 2*(-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^(1/3) + 139/49152)/2 + sqrt(9*a/16 + 2*(-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^(1/3) + 139/24576 - (-9*a^2/32 - 729*a/4096 - 90339/1048576)/sqrt(9*a/32 - 2*(-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^(1/3) + 139/49152))/2 + 27/256, a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296 = 0), (sqrt(9*a/32 + 2*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3) + 139/49152 - 2*(a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)/(3*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3)))/2 + sqrt(9*a/16 - (-9*a^2/32 - 729*a/4096 - 90339/1048576)/sqrt(9*a/32 + 2*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3) + 139/49152 - 2*(a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)/(3*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3))) - 2*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3) + 139/24576 + 2*(a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)/(3*((-27*a/64 - 139/32768)^3/216 - (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/6 + sqrt((-(-27*a/64 - 139/32768)^3/108 + (-27*a/64 - 139/32768)*(-a^3/64 - 243*a^2/16384 - 85219*a/4194304 - 19842003/4294967296)/3 - (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/8)^2/4 + (a^3/64 + 243*a^2/16384 + 85219*a/4194304 - (-27*a/64 - 139/32768)^2/12 + 19842003/4294967296)^3/27) + (-9*a^2/64 - 729*a/8192 - 90339/2097152)^2/16)^(1/3)))/2 + 27/256, True))))