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- La ecuación:
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Ecuación (x+9)^2=36*x
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Ecuación a+120=2000/5
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Ecuación -x/11+x=50/11
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Ecuación x^2+7x+6=0
- Expresar {x} en función de y en la ecuación:
- 12*x+8*y=18
- 8*x+6*y=20
- -2*x+18*y=13
- -11*x-1*y=15
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Expresiones idénticas
- a(x²+(uno /x²))+b(x+(uno /x))=c
- a(x² más (1 dividir por x²)) más b(x más (1 dividir por x)) es igual a c
- a(x² más (uno dividir por x²)) más b(x más (uno dividir por x)) es igual a c
- ax²+1/x²+bx+1/x=c
- a(x²+(1 dividir por x²))+b(x+(1 dividir por x))=c
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Expresiones semejantes
- a(x²+(1/x²))+b(x-(1/x))=c
- a(x²+(1/x²))-b(x+(1/x))=c
- a(x²-(1/x²))+b(x+(1/x))=c
a(x²+(1/x²))+b(x+(1/x))=c la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 1 \ / 1\ a*|x + --| + b*|x + -| = c | 2| \ x/ \ x /
$$a \left(x^{2} + \frac{1}{x^{2}}\right) + b \left(x + \frac{1}{x}\right) = c$$
Gráfica
Respuesta rápida
[src]
/ ________________________________________________________________________________ / / / 2\ / 2\\\ \ ________________________________________________________________________________ / / / 2\ / 2\\\
| / 2 | | |/ ___________________\ | |/ ___________________\ ||| | / 2 | | |/ ___________________\ | |/ ___________________\ |||
| / / / 2\\ / 2\ | | || / 2 2 | | || / 2 2 | ||| | / / / 2\\ / 2\ | | || / 2 2 | | || / 2 2 | |||
| / | |/ ___________________\ || |/ ___________________\ | | | |\b - \/ b + 8*a + 4*a*c / | |\b - \/ b + 8*a + 4*a*c / ||| | / | |/ ___________________\ || |/ ___________________\ | | | |\b - \/ b + 8*a + 4*a*c / | |\b - \/ b + 8*a + 4*a*c / |||
| / | || / 2 2 | || || / 2 2 | | | |im|-----------------------------| re|-----------------------------||| | / | || / 2 2 | || || / 2 2 | | | |im|-----------------------------| re|-----------------------------|||
| / | |\b - \/ b + 8*a + 4*a*c / || 2|\b - \/ b + 8*a + 4*a*c / | | | | 2 | | 2 ||| | / | |\b - \/ b + 8*a + 4*a*c / || 2|\b - \/ b + 8*a + 4*a*c / | | | | 2 | | 2 |||
| / | re|-----------------------------|| im |-----------------------------| | | \ a / \ a /|| / ______________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________ \ | / | re|-----------------------------|| im |-----------------------------| | | \ a / \ a /|| / ______________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________ \
| / | | 2 || | 2 | |atan2|---------------------------------, -4 + ---------------------------------|| | / 2 / / 2 2 2 2 \\| | / 2 / / 2 2 2 2 \\| | / | | 2 || | 2 | |atan2|---------------------------------, -4 + ---------------------------------|| | / 2 / / 2 2 2 2 \\| | / 2 / / 2 2 2 2 \\|
| / | \ a /| \ a / | \ 4 4 /| | 4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/|| | 4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/|| | / | \ a /| \ a / | \ 4 4 /| | 4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/|| | 4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/||
| 4 / |-4 + ---------------------------------| + ---------------------------------- *sin|--------------------------------------------------------------------------------| |-re(b) + \/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *cos|----------------------------------------------------------------------------------------------------||*im(a) |-im(b) + \/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *sin|----------------------------------------------------------------------------------------------------||*re(a)| 4 / |-4 + ---------------------------------| + ---------------------------------- *cos|--------------------------------------------------------------------------------| |-im(b) + \/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *sin|----------------------------------------------------------------------------------------------------||*im(a) |-re(b) + \/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *cos|----------------------------------------------------------------------------------------------------||*re(a)
| \/ \ 4 / 16 \ 2 / \ \ 2 // \ \ 2 // | \/ \ 4 / 16 \ 2 / \ \ 2 // \ \ 2 //
x1 = I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 / 2 2 \ / 2 2 \ | 2 / 2 2 \ / 2 2 \
\ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 4*\im (a) + re (a)/ 4*\im (a) + re (a)/
$$x_{1} = \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(b\right)}\right) \operatorname{im}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(b\right)}\right) \operatorname{re}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(\frac{\operatorname{re}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4\right)^{2} + \frac{\left(\operatorname{im}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}\right)^{2}}{16}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\operatorname{im}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4},\frac{\operatorname{re}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4 \right)}}{2} \right)}}{2} + i \left(\frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(b\right)}\right) \operatorname{re}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(b\right)}\right) \operatorname{im}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(\frac{\operatorname{re}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4\right)^{2} + \frac{\left(\operatorname{im}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}\right)^{2}}{16}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\operatorname{im}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4},\frac{\operatorname{re}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4 \right)}}{2} \right)}}{2}\right)$$
/ ________________________________________________________________________________ / / / 2\ / 2\\\ \ ________________________________________________________________________________ / / / 2\ / 2\\\
| / 2 | | |/ ___________________\ | |/ ___________________\ ||| | / 2 | | |/ ___________________\ | |/ ___________________\ |||
| / / / 2\\ / 2\ | | || / 2 2 | | || / 2 2 | ||| | / / / 2\\ / 2\ | | || / 2 2 | | || / 2 2 | |||
| / | |/ ___________________\ || |/ ___________________\ | | | |\b - \/ b + 8*a + 4*a*c / | |\b - \/ b + 8*a + 4*a*c / ||| | / | |/ ___________________\ || |/ ___________________\ | | | |\b - \/ b + 8*a + 4*a*c / | |\b - \/ b + 8*a + 4*a*c / |||
| / | || / 2 2 | || || / 2 2 | | | |im|-----------------------------| re|-----------------------------||| | / | || / 2 2 | || || / 2 2 | | | |im|-----------------------------| re|-----------------------------|||
| / | |\b - \/ b + 8*a + 4*a*c / || 2|\b - \/ b + 8*a + 4*a*c / | | | | 2 | | 2 ||| | / | |\b - \/ b + 8*a + 4*a*c / || 2|\b - \/ b + 8*a + 4*a*c / | | | | 2 | | 2 |||
| / | re|-----------------------------|| im |-----------------------------| | | \ a / \ a /|| / ______________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________ \ | / | re|-----------------------------|| im |-----------------------------| | | \ a / \ a /|| / ______________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________ \
| / | | 2 || | 2 | |atan2|---------------------------------, -4 + ---------------------------------|| | / 2 / / 2 2 2 2 \\| | / 2 / / 2 2 2 2 \\| | / | | 2 || | 2 | |atan2|---------------------------------, -4 + ---------------------------------|| | / 2 / / 2 2 2 2 \\| | / 2 / / 2 2 2 2 \\|
| / | \ a /| \ a / | \ 4 4 /| | 4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/|| | 4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/|| | / | \ a /| \ a / | \ 4 4 /| | 4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/|| | 4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/||
|4 / |-4 + ---------------------------------| + ---------------------------------- *sin|--------------------------------------------------------------------------------| |-re(b) + \/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *cos|----------------------------------------------------------------------------------------------------||*im(a) |-im(b) + \/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *sin|----------------------------------------------------------------------------------------------------||*re(a)| 4 / |-4 + ---------------------------------| + ---------------------------------- *cos|--------------------------------------------------------------------------------| |-im(b) + \/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *sin|----------------------------------------------------------------------------------------------------||*im(a) |-re(b) + \/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *cos|----------------------------------------------------------------------------------------------------||*re(a)
|\/ \ 4 / 16 \ 2 / \ \ 2 // \ \ 2 // | \/ \ 4 / 16 \ 2 / \ \ 2 // \ \ 2 //
x2 = I*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 / 2 2 \ / 2 2 \ | 2 / 2 2 \ / 2 2 \
\ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 4*\im (a) + re (a)/ 4*\im (a) + re (a)/
$$x_{2} = \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(b\right)}\right) \operatorname{im}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(b\right)}\right) \operatorname{re}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(\frac{\operatorname{re}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4\right)^{2} + \frac{\left(\operatorname{im}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}\right)^{2}}{16}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\operatorname{im}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4},\frac{\operatorname{re}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4 \right)}}{2} \right)}}{2} + i \left(\frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(b\right)}\right) \operatorname{re}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(b\right)}\right) \operatorname{im}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(\frac{\operatorname{re}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4\right)^{2} + \frac{\left(\operatorname{im}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}\right)^{2}}{16}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\operatorname{im}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4},\frac{\operatorname{re}{\left(\frac{\left(b - \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4 \right)}}{2} \right)}}{2}\right)$$
/ ________________________________________________________________________________ / / / 2\ / 2\\\ \ ________________________________________________________________________________ / / / 2\ / 2\\\
| / 2 | | |/ ___________________\ | |/ ___________________\ ||| | / 2 | | |/ ___________________\ | |/ ___________________\ |||
| / / / 2\\ / 2\ | | || / 2 2 | | || / 2 2 | ||| | / / / 2\\ / 2\ | | || / 2 2 | | || / 2 2 | |||
| / | |/ ___________________\ || |/ ___________________\ | | | |\b + \/ b + 8*a + 4*a*c / | |\b + \/ b + 8*a + 4*a*c / ||| | / | |/ ___________________\ || |/ ___________________\ | | | |\b + \/ b + 8*a + 4*a*c / | |\b + \/ b + 8*a + 4*a*c / |||
| / | || / 2 2 | || || / 2 2 | | | |im|-----------------------------| re|-----------------------------||| | / | || / 2 2 | || || / 2 2 | | | |im|-----------------------------| re|-----------------------------|||
| / | |\b + \/ b + 8*a + 4*a*c / || 2|\b + \/ b + 8*a + 4*a*c / | | | | 2 | | 2 ||| | / | |\b + \/ b + 8*a + 4*a*c / || 2|\b + \/ b + 8*a + 4*a*c / | | | | 2 | | 2 |||
| / | re|-----------------------------|| im |-----------------------------| | | \ a / \ a /|| / ______________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________ \ | / | re|-----------------------------|| im |-----------------------------| | | \ a / \ a /|| / ______________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________ \
| / | | 2 || | 2 | |atan2|---------------------------------, -4 + ---------------------------------|| | / 2 / / 2 2 2 2 \\ | | / 2 / / 2 2 2 2 \\ | | / | | 2 || | 2 | |atan2|---------------------------------, -4 + ---------------------------------|| | / 2 / / 2 2 2 2 \\ | | / 2 / / 2 2 2 2 \\ |
| / | \ a /| \ a / | \ 4 4 /| |4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/| | |4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/| | | / | \ a /| \ a / | \ 4 4 /| |4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/| | |4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/| |
| 4 / |-4 + ---------------------------------| + ---------------------------------- *sin|--------------------------------------------------------------------------------| |\/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *sin|----------------------------------------------------------------------------------------------------| + im(b)|*re(a) |\/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *cos|----------------------------------------------------------------------------------------------------| + re(b)|*im(a)| 4 / |-4 + ---------------------------------| + ---------------------------------- *cos|--------------------------------------------------------------------------------| |\/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *cos|----------------------------------------------------------------------------------------------------| + re(b)|*re(a) |\/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *sin|----------------------------------------------------------------------------------------------------| + im(b)|*im(a)
| \/ \ 4 / 16 \ 2 / \ \ 2 / / \ \ 2 / / | \/ \ 4 / 16 \ 2 / \ \ 2 / / \ \ 2 / /
x3 = I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 / 2 2 \ / 2 2 \ | 2 / 2 2 \ / 2 2 \
\ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 4*\im (a) + re (a)/ 4*\im (a) + re (a)/
$$x_{3} = - \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(b\right)}\right) \operatorname{im}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(b\right)}\right) \operatorname{re}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(\frac{\operatorname{re}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4\right)^{2} + \frac{\left(\operatorname{im}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}\right)^{2}}{16}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\operatorname{im}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4},\frac{\operatorname{re}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4 \right)}}{2} \right)}}{2} + i \left(- \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(b\right)}\right) \operatorname{re}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(b\right)}\right) \operatorname{im}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(\frac{\operatorname{re}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4\right)^{2} + \frac{\left(\operatorname{im}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}\right)^{2}}{16}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\operatorname{im}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4},\frac{\operatorname{re}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4 \right)}}{2} \right)}}{2}\right)$$
/ ________________________________________________________________________________ / / / 2\ / 2\\\ \ ________________________________________________________________________________ / / / 2\ / 2\\\
| / 2 | | |/ ___________________\ | |/ ___________________\ ||| | / 2 | | |/ ___________________\ | |/ ___________________\ |||
| / / / 2\\ / 2\ | | || / 2 2 | | || / 2 2 | ||| | / / / 2\\ / 2\ | | || / 2 2 | | || / 2 2 | |||
| / | |/ ___________________\ || |/ ___________________\ | | | |\b + \/ b + 8*a + 4*a*c / | |\b + \/ b + 8*a + 4*a*c / ||| | / | |/ ___________________\ || |/ ___________________\ | | | |\b + \/ b + 8*a + 4*a*c / | |\b + \/ b + 8*a + 4*a*c / |||
| / | || / 2 2 | || || / 2 2 | | | |im|-----------------------------| re|-----------------------------||| | / | || / 2 2 | || || / 2 2 | | | |im|-----------------------------| re|-----------------------------|||
| / | |\b + \/ b + 8*a + 4*a*c / || 2|\b + \/ b + 8*a + 4*a*c / | | | | 2 | | 2 ||| | / | |\b + \/ b + 8*a + 4*a*c / || 2|\b + \/ b + 8*a + 4*a*c / | | | | 2 | | 2 |||
| / | re|-----------------------------|| im |-----------------------------| | | \ a / \ a /|| / ______________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________ \ | / | re|-----------------------------|| im |-----------------------------| | | \ a / \ a /|| / ______________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________ \
| / | | 2 || | 2 | |atan2|---------------------------------, -4 + ---------------------------------|| | / 2 / / 2 2 2 2 \\ | | / 2 / / 2 2 2 2 \\ | | / | | 2 || | 2 | |atan2|---------------------------------, -4 + ---------------------------------|| | / 2 / / 2 2 2 2 \\ | | / 2 / / 2 2 2 2 \\ |
| / | \ a /| \ a / | \ 4 4 /| |4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/| | |4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/| | | / | \ a /| \ a / | \ 4 4 /| |4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/| | |4 / 2 / 2 2 2 2 \ |atan2\4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a), re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/| |
|4 / |-4 + ---------------------------------| + ---------------------------------- *sin|--------------------------------------------------------------------------------| |\/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *sin|----------------------------------------------------------------------------------------------------| + im(b)|*re(a) |\/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *cos|----------------------------------------------------------------------------------------------------| + re(b)|*im(a)| 4 / |-4 + ---------------------------------| + ---------------------------------- *cos|--------------------------------------------------------------------------------| |\/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *cos|----------------------------------------------------------------------------------------------------| + re(b)|*re(a) |\/ (4*im(a*c) + 2*im(b)*re(b) + 16*im(a)*re(a)) + \re (b) - im (b) - 8*im (a) + 4*re(a*c) + 8*re (a)/ *sin|----------------------------------------------------------------------------------------------------| + im(b)|*im(a)
|\/ \ 4 / 16 \ 2 / \ \ 2 / / \ \ 2 / / | \/ \ 4 / 16 \ 2 / \ \ 2 / / \ \ 2 / /
x4 = I*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 / 2 2 \ / 2 2 \ | 2 / 2 2 \ / 2 2 \
\ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 4*\im (a) + re (a)/ 4*\im (a) + re (a)/
$$x_{4} = - \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(b\right)}\right) \operatorname{im}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(b\right)}\right) \operatorname{re}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(\frac{\operatorname{re}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4\right)^{2} + \frac{\left(\operatorname{im}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}\right)^{2}}{16}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\operatorname{im}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4},\frac{\operatorname{re}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4 \right)}}{2} \right)}}{2} + i \left(- \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(b\right)}\right) \operatorname{re}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)}\right)^{2} + \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a c\right)},8 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + 4 \operatorname{re}{\left(a c\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(b\right)}\right) \operatorname{im}{\left(a\right)}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(\frac{\operatorname{re}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4\right)^{2} + \frac{\left(\operatorname{im}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}\right)^{2}}{16}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\operatorname{im}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4},\frac{\operatorname{re}{\left(\frac{\left(b + \sqrt{8 a^{2} + 4 a c + b^{2}}\right)^{2}}{a^{2}}\right)}}{4} - 4 \right)}}{2} \right)}}{2}\right)$$
x4 = -(((16*re(a)*im(a) + 2*re(b)*im(b) + 4*im(a*c))^2 + (8*re(a)^2 + re(b)^2 + 4*re(a*c) - 8*im(a)^2 - im(b)^2)^2)^(1/4)*sin(atan2(16*re(a)*im(a) + 2*re(b)*im(b) + 4*im(a*c, 8*re(a)^2 + re(b)^2 + 4*re(a*c) - 8*im(a)^2 - im(b)^2)/2) + im(b))*im(a)/(4*(re(a)^2 + im(a)^2)) - (((16*re(a)*im(a) + 2*re(b)*im(b) + 4*im(a*c))^2 + (8*re(a)^2 + re(b)^2 + 4*re(a*c) - 8*im(a)^2 - im(b)^2)^2)^(1/4)*cos(atan2(16*re(a)*im(a) + 2*re(b)*im(b) + 4*im(a*c), 8*re(a)^2 + re(b)^2 + 4*re(a*c) - 8*im(a)^2 - im(b)^2)/2) + re(b))*re(a)/(4*(re(a)^2 + im(a)^2)) + ((re((b + sqrt(8*a^2 + 4*a*c + b^2))^2/a^2)/4 - 4)^2 + im((b + sqrt(8*a^2 + 4*a*c + b^2))^2/a^2)^2/16)^(1/4)*cos(atan2(im((b + sqrt(8*a^2 + 4*a*c + b^2))^2/a^2)/4, re((b + sqrt(8*a^2 + 4*a*c + b^2))^2/a^2)/4 - 4)/2)/2 + i*(-(((16*re(a)*im(a) + 2*re(b)*im(b) + 4*im(a*c))^2 + (8*re(a)^2 + re(b)^2 + 4*re(a*c) - 8*im(a)^2 - im(b)^2)^2)^(1/4)*sin(atan2(16*re(a)*im(a) + 2*re(b)*im(b) + 4*im(a*c), 8*re(a)^2 + re(b)^2 + 4*re(a*c) - 8*im(a)^2 - im(b)^2)/2) + im(b))*re(a)/(4*(re(a)^2 + im(a)^2)) + (((16*re(a)*im(a) + 2*re(b)*im(b) + 4*im(a*c))^2 + (8*re(a)^2 + re(b)^2 + 4*re(a*c) - 8*im(a)^2 - im(b)^2)^2)^(1/4)*cos(atan2(16*re(a)*im(a) + 2*re(b)*im(b) + 4*im(a*c), 8*re(a)^2 + re(b)^2 + 4*re(a*c) - 8*im(a)^2 - im(b)^2)/2) + re(b))*im(a)/(4*(re(a)^2 + im(a)^2)) + ((re((b + sqrt(8*a^2 + 4*a*c + b^2))^2/a^2)/4 - 4)^2 + im((b + sqrt(8*a^2 + 4*a*c + b^2))^2/a^2)^2/16)^(1/4)*sin(atan2(im((b + sqrt(8*a^2 + 4*a*c + b^2))^2/a^2)/4, re((b + sqrt(8*a^2 + 4*a*c + b^2))^2/a^2)/4 - 4)/2)/2))