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- La ecuación:
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Ecuación x^4+2*x^2-8=0
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Ecuación x*(x^2+8*x+16)=5*(x+4)
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Ecuación ((57.6/(150-x))^0.15)*((150+x)+10)/171.712=1
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Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
- Límite de la función:
- f*x
- Derivada de:
- f*x
- Integral de d{x}:
- f*x
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Expresiones idénticas
- f*x=(tres *x^ cuatro - cuatro *x^ tres - cinco *x+ doce)/x
- f multiplicar por x es igual a (3 multiplicar por x en el grado 4 menos 4 multiplicar por x al cubo menos 5 multiplicar por x más 12) dividir por x
- f multiplicar por x es igual a (tres multiplicar por x en el grado cuatro menos cuatro multiplicar por x en el grado tres menos cinco multiplicar por x más doce) dividir por x
- f*x=(3*x4-4*x3-5*x+12)/x
- f*x=3*x4-4*x3-5*x+12/x
- f*x=(3*x⁴-4*x³-5*x+12)/x
- f*x=(3*x en el grado 4-4*x en el grado 3-5*x+12)/x
- fx=(3x^4-4x^3-5x+12)/x
- fx=(3x4-4x3-5x+12)/x
- fx=3x4-4x3-5x+12/x
- fx=3x^4-4x^3-5x+12/x
- f*x=(3*x^4-4*x^3-5*x+12) dividir por x
-
Expresiones semejantes
- f*(x)=log((x-3)/(x+1))
- x.diff(x)=(2*sin(t))*x+(log(t))*y
- f*x=(3*x^4-4*x^3-5*x-12)/x
- y*x.diff(x)+x=-y*x^2
- f*x=(3*x^4+4*x^3-5*x+12)/x
- erf(x)=0.5
- f*x=(3*x^4-4*x^3+5*x+12)/x
f*x=(3*x^4-4*x^3-5*x+12)/x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 3
3*x - 4*x - 5*x + 12
f*x = ----------------------
x
$$f x = \frac{\left(- 5 x + \left(3 x^{4} - 4 x^{3}\right)\right) + 12}{x}$$
Gráfica
Respuesta rápida
[src]
// _____________________________________________________________________________________________________________________________________________________________ \ // _____________________________________________________________________________________________________________________________________________________________ \
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|| / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | || / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f |
|| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- | || / / |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- |
|| / 8 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 | || / 8 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 |
|| / - + 2*3 / - ------------- - ---------- + ------------------- + --- + --------------------------------------------------------------------------------- | || / - + 2*3 / - ------------- - ---------- + ------------------- + --- + --------------------------------------------------------------------------------- |
|| _________________________________________________________________________ / 9 \/ 8 108 3 9 _________________________________________________________________________ | || _________________________________________________________________________ / 9 \/ 8 108 3 9 _________________________________________________________________________ |
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|| / / 2 3 / / / 2 3 | || / / 2 3 / / / 2 3 |
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|| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / |- -- - ---| |- - - -| |- - - -|*|-- - --| 2 | || / / |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / |- -- - ---| |- - - -| |- - - -|*|-- - --| 2 |
|| / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 2 f\ | || / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 2 f\ |
|| / - - 2*3 / - ------------- - ---------- + ------------------- + --- / / - - 2*3 / - ------------- - ---------- + ------------------- + --- |- - - -| | || / - - 2*3 / - ------------- - ---------- + ------------------- + --- / / - - 2*3 / - ------------- - ---------- + ------------------- + --- |- - - -| |
|| 1 \/ 9 \/ 8 108 3 9 \/ \/ 9 \/ 8 108 3 9 92 f \ 3 3/ | || 1 \/ 9 \/ 8 108 3 9 \/ \/ 9 \/ 8 108 3 9 92 f \ 3 3/ |
|| - - --------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for -- - -- + ---------- = 0| || - - --------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for -- - -- + ---------- = 0|
|| 3 2 2 27 27 12 | || 3 2 2 27 27 12 |
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|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | 92 \ 3 3/ f | | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | 92 \ 3 3/ f | |
x1 = I*im|< / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- 2*|- -- - ---------- + --| | + re|< / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- 2*|- -- - ---------- + --| |
|| / 8 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 \ 27 12 27/ | || / 8 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 \ 27 12 27/ |
|| / - - 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / - - 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 9 \/ \/ 4 27 16 216 6 9 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 9 \/ \/ 4 27 16 216 6 9 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ |
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|| / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ / / 2 3 | || / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ / / 2 3 |
|| / / / 2 3 / / / / 2 3 / / / 2 3 \ / 2 \ | || / / / 2 3 / / / / 2 3 / / / 2 3 \ / 2 \ |
|| / / / / 2 3 \ / 2 \ / 2 \ / / / / / 2 3 \ / 2 \ / 2 \ / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | || / / / / 2 3 \ / 2 \ / 2 \ / / / / / 2 3 \ / 2 \ / 2 \ / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | |
|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| |
|| / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ | || / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ |
|| / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ / / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- | || / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ / / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- |
|| / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- / / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 | || / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- / / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 |
|| / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ / / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ | || / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ / / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ |
|| / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ | || / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ |
|| / / / 2 3 / / / / 2 3 | || / / / 2 3 / / / / 2 3 |
|| / / / / 2 3 \ / 2 \ / / / / / 2 3 \ / 2 \ | || / / / / 2 3 \ / 2 \ / / / / / 2 3 \ / 2 \ |
|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| | || / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| |
|| / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ | || / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ |
|| / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- | || / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- |
||1 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 | ||1 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 |
||- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\3 2 2 / \\3 2 2 /
$$x_{1} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}}{2} - \frac{\sqrt{\frac{4 f}{9} + \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}} + 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{for}\: - \frac{f}{27} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} + \frac{92}{27} = 0 \\- \frac{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}}{2} - \frac{\sqrt{\frac{4 f}{9} + \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}} + \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} - 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}}{2} - \frac{\sqrt{\frac{4 f}{9} + \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}} + 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{for}\: - \frac{f}{27} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} + \frac{92}{27} = 0 \\- \frac{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}}{2} - \frac{\sqrt{\frac{4 f}{9} + \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}} + \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} - 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{otherwise} \end{cases}\right)}$$
// _____________________________________________________________________________________________________________________________________________________________ \ // _____________________________________________________________________________________________________________________________________________________________ \
|| / ____________________________________________________ | || / ____________________________________________________ |
|| / / 2 3 | || / / 2 3 |
|| / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | || / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f |
|| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- | || / / |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- |
|| / 8 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 | || / 8 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 |
|| / - + 2*3 / - ------------- - ---------- + ------------------- + --- + --------------------------------------------------------------------------------- | || / - + 2*3 / - ------------- - ---------- + ------------------- + --- + --------------------------------------------------------------------------------- |
|| / 9 \/ 8 108 3 9 _________________________________________________________________________ _________________________________________________________________________ | || / 9 \/ 8 108 3 9 _________________________________________________________________________ _________________________________________________________________________ |
|| / / ____________________________________________________ / ____________________________________________________ | || / / ____________________________________________________ / ____________________________________________________ |
|| / / / 2 3 / / 2 3 | || / / / 2 3 / / 2 3 |
|| / / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / / |- -- - ---| |- - - -| |- - - -|*|-- - --| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| 2 | || / / / |- -- - ---| |- - - -| |- - - -|*|-- - --| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| 2 |
|| / / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 2 f\ | || / / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 2 f\ |
|| / / - - 2*3 / - ------------- - ---------- + ------------------- + --- / - - 2*3 / - ------------- - ---------- + ------------------- + --- |- - - -| | || / / - - 2*3 / - ------------- - ---------- + ------------------- + --- / - - 2*3 / - ------------- - ---------- + ------------------- + --- |- - - -| |
|| 1 \/ \/ 9 \/ 8 108 3 9 \/ 9 \/ 8 108 3 9 92 f \ 3 3/ | || 1 \/ \/ 9 \/ 8 108 3 9 \/ 9 \/ 8 108 3 9 92 f \ 3 3/ |
|| - + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------- for -- - -- + ---------- = 0| || - + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------- for -- - -- + ---------- = 0|
|| 3 2 2 27 27 12 | || 3 2 2 27 27 12 |
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|| ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
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|| / / / 2 3 | || / / / 2 3 |
|| / / / / 2 3 \ / 2 \ / 2 \ | || / / / / 2 3 \ / 2 \ / 2 \ |
|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | 92 \ 3 3/ f | | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | 92 \ 3 3/ f | |
x2 = I*im|< / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- 2*|- -- - ---------- + --| | + re|< / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- 2*|- -- - ---------- + --| |
|| / 8 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 \ 27 12 27/ | || / 8 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 \ 27 12 27/ |
|| / - - 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / - - 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| / 9 \/ \/ 4 27 16 216 6 9 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || / 9 \/ \/ 4 27 16 216 6 9 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / __________________________________________________________________________________________________________________________________________________ / ___________________________________________________________________________________ / __________________________________________________________________________________________________________________________________________________ | || / / __________________________________________________________________________________________________________________________________________________ / ___________________________________________________________________________________ / __________________________________________________________________________________________________________________________________________________ |
|| / / / ___________________________________________________________________________________ / / 2 3 / / ___________________________________________________________________________________ | || / / / ___________________________________________________________________________________ / / 2 3 / / ___________________________________________________________________________________ |
|| / / / / 2 3 / / / 2 3 \ / 2 \ / / / 2 3 | || / / / / 2 3 / / / 2 3 \ / 2 \ / / / 2 3 |
|| / / / / / 2 3 \ / 2 \ / 2 \ / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / / 2 3 \ / 2 \ / 2 \ | || / / / / / 2 3 \ / 2 \ / 2 \ / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / / 2 3 \ / 2 \ / 2 \ |
|| / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | | || / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | |
|| / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | | || / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | |
|| / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | | || / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | |
|| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| | || / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| |
|| / / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ | || / / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ |
|| / / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| / / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ | || / / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ |
|| / / / ___________________________________________________________________________________ / / ___________________________________________________________________________________ | || / / / ___________________________________________________________________________________ / / ___________________________________________________________________________________ |
|| / / / / 2 3 / / / 2 3 | || / / / / 2 3 / / / 2 3 |
|| / / / / / 2 3 \ / 2 \ / / / / 2 3 \ / 2 \ | || / / / / / 2 3 \ / 2 \ / / / / 2 3 \ / 2 \ |
|| / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | || / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | |
|| / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | || / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 |
|| / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| | || / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| |
|| / / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ | || / / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ |
|| / / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- | || / / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- |
||1 \/ \/ \/ \/ 4 27 16 216 6 \/ \/ \/ 4 27 16 216 6 | ||1 \/ \/ \/ \/ 4 27 16 216 6 \/ \/ \/ 4 27 16 216 6 |
||- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\3 2 2 / \\3 2 2 /
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}}{2} + \frac{\sqrt{\frac{4 f}{9} + \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}} + 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{for}\: - \frac{f}{27} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} + \frac{92}{27} = 0 \\- \frac{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}}{2} + \frac{\sqrt{\frac{4 f}{9} + \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}} + \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} - 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}}{2} + \frac{\sqrt{\frac{4 f}{9} + \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}} + 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{for}\: - \frac{f}{27} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} + \frac{92}{27} = 0 \\- \frac{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}}{2} + \frac{\sqrt{\frac{4 f}{9} + \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}} + \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} - 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{otherwise} \end{cases}\right)}$$
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|| / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | || / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f |
|| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- | || / / |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- |
|| / 8 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 | || / 8 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 |
|| / - + 2*3 / - ------------- - ---------- + ------------------- + --- - --------------------------------------------------------------------------------- | || / - + 2*3 / - ------------- - ---------- + ------------------- + --- - --------------------------------------------------------------------------------- |
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|| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / |- -- - ---| |- - - -| |- - - -|*|-- - --| 2 | || / / |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / |- -- - ---| |- - - -| |- - - -|*|-- - --| 2 |
|| / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 2 f\ | || / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 2 f\ |
|| / - - 2*3 / - ------------- - ---------- + ------------------- + --- / / - - 2*3 / - ------------- - ---------- + ------------------- + --- |- - - -| | || / - - 2*3 / - ------------- - ---------- + ------------------- + --- / / - - 2*3 / - ------------- - ---------- + ------------------- + --- |- - - -| |
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|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | 92 \ 3 3/ f | | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | 92 \ 3 3/ f | |
x3 = I*im|< / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- 2*|- -- - ---------- + --| | + re|< / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- 2*|- -- - ---------- + --| |
|| / 8 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 \ 27 12 27/ | || / 8 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 \ 27 12 27/ |
|| / - - 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / - - 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 9 \/ \/ 4 27 16 216 6 9 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 9 \/ \/ 4 27 16 216 6 9 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ |
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|| / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ / / 2 3 | || / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ / / 2 3 |
|| / / / 2 3 / / / / 2 3 / / / 2 3 \ / 2 \ | || / / / 2 3 / / / / 2 3 / / / 2 3 \ / 2 \ |
|| / / / / 2 3 \ / 2 \ / 2 \ / / / / / 2 3 \ / 2 \ / 2 \ / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | || / / / / 2 3 \ / 2 \ / 2 \ / / / / / 2 3 \ / 2 \ / 2 \ / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | |
|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| |
|| / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ | || / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ |
|| / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ / / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- | || / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ / / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- |
|| / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- / / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 | || / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- / / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 |
|| / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ / / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ | || / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ / / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ |
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|| / / / 2 3 / / / / 2 3 | || / / / 2 3 / / / / 2 3 |
|| / / / / 2 3 \ / 2 \ / / / / / 2 3 \ / 2 \ | || / / / / 2 3 \ / 2 \ / / / / / 2 3 \ / 2 \ |
|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| | || / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| |
|| / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ | || / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ |
|| / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- | || / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- |
||1 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 | ||1 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 |
||- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\3 2 2 / \\3 2 2 /
$$x_{3} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}}{2} - \frac{\sqrt{\frac{4 f}{9} - \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}} + 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{for}\: - \frac{f}{27} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} + \frac{92}{27} = 0 \\\frac{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}}{2} - \frac{\sqrt{\frac{4 f}{9} - \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}} + \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} - 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}}{2} - \frac{\sqrt{\frac{4 f}{9} - \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}} + 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{for}\: - \frac{f}{27} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} + \frac{92}{27} = 0 \\\frac{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}}{2} - \frac{\sqrt{\frac{4 f}{9} - \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}} + \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} - 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{otherwise} \end{cases}\right)}$$
// _____________________________________________________________________________________________________________________________________________________________ \ // _____________________________________________________________________________________________________________________________________________________________ \
|| / ____________________________________________________ | || / ____________________________________________________ |
|| / / 2 3 | || / / 2 3 |
|| / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | || / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f |
|| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- | || / / |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- |
|| / 8 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 | || / 8 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 |
|| / - + 2*3 / - ------------- - ---------- + ------------------- + --- - --------------------------------------------------------------------------------- | || / - + 2*3 / - ------------- - ---------- + ------------------- + --- - --------------------------------------------------------------------------------- |
|| _________________________________________________________________________ / 9 \/ 8 108 3 9 _________________________________________________________________________ | || _________________________________________________________________________ / 9 \/ 8 108 3 9 _________________________________________________________________________ |
|| / ____________________________________________________ / / ____________________________________________________ | || / ____________________________________________________ / / ____________________________________________________ |
|| / / 2 3 / / / 2 3 | || / / 2 3 / / / 2 3 |
|| / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / |- -- - ---| |- - - -| |- - - -|*|-- - --| 2 | || / / |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / |- -- - ---| |- - - -| |- - - -|*|-- - --| 2 |
|| / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 2 f\ | || / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / / 4 / \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f / 2 f\ |
|| / - - 2*3 / - ------------- - ---------- + ------------------- + --- / / - - 2*3 / - ------------- - ---------- + ------------------- + --- |- - - -| | || / - - 2*3 / - ------------- - ---------- + ------------------- + --- / / - - 2*3 / - ------------- - ---------- + ------------------- + --- |- - - -| |
|| 1 \/ 9 \/ 8 108 3 9 \/ \/ 9 \/ 8 108 3 9 92 f \ 3 3/ | || 1 \/ 9 \/ 8 108 3 9 \/ \/ 9 \/ 8 108 3 9 92 f \ 3 3/ |
|| - + --------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for -- - -- + ---------- = 0| || - + --------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for -- - -- + ---------- = 0|
|| 3 2 2 27 27 12 | || 3 2 2 27 27 12 |
|| | || |
|| ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / __________________________________________________________________________________________________________________________________________________ | || / __________________________________________________________________________________________________________________________________________________ |
|| / / ___________________________________________________________________________________ | || / / ___________________________________________________________________________________ |
|| / / / 2 3 | || / / / 2 3 |
|| / / / / 2 3 \ / 2 \ / 2 \ | || / / / / 2 3 \ / 2 \ / 2 \ |
|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | 92 \ 3 3/ f | | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ 106 4*f | 92 \ 3 3/ f | |
x4 = I*im|< / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- 2*|- -- - ---------- + --| | + re|< / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| - --- - --- 2*|- -- - ---------- + --| |
|| / 8 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 \ 27 12 27/ | || / 8 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 4*f 27 9 \ 27 12 27/ |
|| / - - 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------- | || / - - 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------- |
|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 9 \/ \/ 4 27 16 216 6 9 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ | || _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / 9 \/ \/ 4 27 16 216 6 9 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ |
|| / __________________________________________________________________________________________________________________________________________________ / / __________________________________________________________________________________________________________________________________________________ / ___________________________________________________________________________________ | || / __________________________________________________________________________________________________________________________________________________ / / __________________________________________________________________________________________________________________________________________________ / ___________________________________________________________________________________ |
|| / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ / / 2 3 | || / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ / / 2 3 |
|| / / / 2 3 / / / / 2 3 / / / 2 3 \ / 2 \ | || / / / 2 3 / / / / 2 3 / / / 2 3 \ / 2 \ |
|| / / / / 2 3 \ / 2 \ / 2 \ / / / / / 2 3 \ / 2 \ / 2 \ / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | || / / / / 2 3 \ / 2 \ / 2 \ / / / / / 2 3 \ / 2 \ / 2 \ / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | |
|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | / 2 f\ | / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | |- - - -| | / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | 92 \ 3 3/ f | / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| |
|| / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ | || / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| 2*|- -- - ---------- + --| / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ |
|| / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ / / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- | || / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ / / 4 / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ 2*f \ 27 12 27/ 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- |
|| / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- / / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 | || / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- / / - + 2*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- + --- - --------------------------------------------------------------------------------------------------------------------------------------------------------------- \/ \/ 4 27 16 216 6 |
|| / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ / / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ | || / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ / / 9 \/ \/ 4 27 16 216 6 9 __________________________________________________________________________________________________________________________________________________ |
|| / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ | || / / ___________________________________________________________________________________ / / / ___________________________________________________________________________________ |
|| / / / 2 3 / / / / 2 3 | || / / / 2 3 / / / / 2 3 |
|| / / / / 2 3 \ / 2 \ / / / / / 2 3 \ / 2 \ | || / / / / 2 3 \ / 2 \ / / / / / 2 3 \ / 2 \ |
|| / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | | || / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | / / / / | / 53 2*f\ / 2 f\ / 2 f\ /92 f \| | / 2 f\ | |
|| / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 | || / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 / / / / | |- -- - ---| |- - - -| |- - - -|*|-- - --|| | |- - - -| | 2 3 |
|| / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ | || / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ / / / / | \ 27 9 / \ 3 3/ \ 3 3/ \27 27/| | 92 \ 3 3/ f | / 53 2*f\ / 2 f\ / 2 f\ /92 f \ |
|| / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| | || / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| / / / / |- ------------- - ---------- + -------------------| |- -- - ---------- + --| |- -- - ---| |- - - -| |- - - -|*|-- - --| |
|| / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ | || / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ / / / / \ 8 108 3 / \ 27 12 27/ \ 27 9 / \ 3 3/ \ 3 3/ \27 27/ |
|| / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- | || / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- / / 3*3 / / ----------------------------------------------------- + ------------------------- + ------------- + ---------- - ------------------- |
||1 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 | ||1 \/ \/ \/ 4 27 16 216 6 \/ \/ \/ \/ 4 27 16 216 6 |
||- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\3 2 2 / \\3 2 2 /
$$x_{4} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}}{2} + \frac{\sqrt{\frac{4 f}{9} - \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}} + 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{for}\: - \frac{f}{27} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} + \frac{92}{27} = 0 \\\frac{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}}{2} + \frac{\sqrt{\frac{4 f}{9} - \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}} + \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} - 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}}{2} + \frac{\sqrt{\frac{4 f}{9} - \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{4}{9}}} + 2 \sqrt[3]{\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{for}\: - \frac{f}{27} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} + \frac{92}{27} = 0 \\\frac{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}}{2} + \frac{\sqrt{\frac{4 f}{9} - \frac{- \frac{4 f}{9} - \frac{106}{27}}{\sqrt{\frac{2 f}{9} - \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} + 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{4}{9}}} + \frac{2 \left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)}{3 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}}} - 2 \sqrt[3]{- \frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{6} + \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{216} + \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{16} + \sqrt{\frac{\left(\frac{f}{27} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{2}}{12} - \frac{92}{27}\right)^{3}}{27} + \frac{\left(\frac{\left(\frac{92}{27} - \frac{f}{27}\right) \left(- \frac{f}{3} - \frac{2}{3}\right)}{3} - \frac{\left(- \frac{f}{3} - \frac{2}{3}\right)^{3}}{108} - \frac{\left(- \frac{2 f}{9} - \frac{53}{27}\right)^{2}}{8}\right)^{2}}{4}}} + \frac{8}{9}}}{2} + \frac{1}{3} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((sqrt(2*f/9 - 2*((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^(1/3) + 4/9)/2 + sqrt(4*f/9 - (-4*f/9 - 106/27)/sqrt(2*f/9 - 2*((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^(1/3) + 4/9) + 2*((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^(1/3) + 8/9/2 + 1/3, -f/27 + (-f/3 - 2/3)^2/12 + 92/27 = 0), (sqrt(2*f/9 - 2*(f/27 - (-f/3 - 2/3)^2/12 - 92/27)/(3*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3)) + 2*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3) + 4/9)/2 + sqrt(4*f/9 - (-4*f/9 - 106/27)/sqrt(2*f/9 - 2*(f/27 - (-f/3 - 2/3)^2/12 - 92/27)/(3*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3)) + 2*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3) + 4/9) + 2*(f/27 - (-f/3 - 2/3)^2/12 - 92/27)/(3*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3)) - 2*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3) + 8/9)/2 + 1/3, True))) + i*im(Piecewise((sqrt(2*f/9 - 2*((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^(1/3) + 4/9)/2 + sqrt(4*f/9 - (-4*f/9 - 106/27)/sqrt(2*f/9 - 2*((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^(1/3) + 4/9) + 2*((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^(1/3) + 8/9)/2 + 1/3, -f/27 + (-f/3 - 2/3)^2/12 + 92/27 = 0), (sqrt(2*f/9 - 2*(f/27 - (-f/3 - 2/3)^2/12 - 92/27)/(3*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3)) + 2*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3) + 4/9)/2 + sqrt(4*f/9 - (-4*f/9 - 106/27)/sqrt(2*f/9 - 2*(f/27 - (-f/3 - 2/3)^2/12 - 92/27)/(3*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3)) + 2*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3) + 4/9) + 2*(f/27 - (-f/3 - 2/3)^2/12 - 92/27)/(3*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3)) - 2*(-(92/27 - f/27)*(-f/3 - 2/3)/6 + (-f/3 - 2/3)^3/216 + (-2*f/9 - 53/27)^2/16 + sqrt((f/27 - (-f/3 - 2/3)^2/12 - 92/27)^3/27 + ((92/27 - f/27)*(-f/3 - 2/3)/3 - (-f/3 - 2/3)^3/108 - (-2*f/9 - 53/27)^2/8)^2/4))^(1/3) + 8/9)/2 + 1/3, True))))