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x^2-6xy+8y^2-3x-12 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 x - 6*x*y + 8*y - 3*x - 12 = 0
$$\left(- 3 x + \left(8 y^{2} + \left(x^{2} - 6 x y\right)\right)\right) - 12 = 0$$
Solución detallada
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 8$$
$$b = - 6 x$$
$$c = x^{2} - 3 x - 12$$
, entonces
La ecuación tiene dos raíces.
o
$$y_{1} = \frac{3 x}{8} + \frac{\sqrt{4 x^{2} + 96 x + 384}}{16}$$
$$y_{2} = \frac{3 x}{8} - \frac{\sqrt{4 x^{2} + 96 x + 384}}{16}$$
a*y^2 + b*y + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 8$$
$$b = - 6 x$$
$$c = x^{2} - 3 x - 12$$
, entonces
D = b^2 - 4 * a * c =
(-6*x)^2 - 4 * (8) * (-12 + x^2 - 3*x) = 384 + 4*x^2 + 96*x
La ecuación tiene dos raíces.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
o
$$y_{1} = \frac{3 x}{8} + \frac{\sqrt{4 x^{2} + 96 x + 384}}{16}$$
$$y_{2} = \frac{3 x}{8} - \frac{\sqrt{4 x^{2} + 96 x + 384}}{16}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- 3 x + \left(8 y^{2} + \left(x^{2} - 6 x y\right)\right)\right) - 12 = 0$$
de
$$a y^{2} + b y + c = 0$$
como ecuación cuadrática reducida
$$y^{2} + \frac{b y}{a} + \frac{c}{a} = 0$$
$$\frac{x^{2}}{8} - \frac{3 x y}{4} - \frac{3 x}{8} + y^{2} - \frac{3}{2} = 0$$
$$p y + q + y^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{3 x}{4}$$
$$q = \frac{c}{a}$$
$$q = \frac{x^{2}}{8} - \frac{3 x}{8} - \frac{3}{2}$$
Fórmulas de Cardano-Vieta
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = \frac{3 x}{4}$$
$$y_{1} y_{2} = \frac{x^{2}}{8} - \frac{3 x}{8} - \frac{3}{2}$$
$$\left(- 3 x + \left(8 y^{2} + \left(x^{2} - 6 x y\right)\right)\right) - 12 = 0$$
de
$$a y^{2} + b y + c = 0$$
como ecuación cuadrática reducida
$$y^{2} + \frac{b y}{a} + \frac{c}{a} = 0$$
$$\frac{x^{2}}{8} - \frac{3 x y}{4} - \frac{3 x}{8} + y^{2} - \frac{3}{2} = 0$$
$$p y + q + y^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{3 x}{4}$$
$$q = \frac{c}{a}$$
$$q = \frac{x^{2}}{8} - \frac{3 x}{8} - \frac{3}{2}$$
Fórmulas de Cardano-Vieta
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = \frac{3 x}{4}$$
$$y_{1} y_{2} = \frac{x^{2}}{8} - \frac{3 x}{8} - \frac{3}{2}$$
Gráfica
Suma y producto de raíces
[src]
suma
/ __________________________________________________________________ \ __________________________________________________________________ / __________________________________________________________________ \ __________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/| | 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|
| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *sin|----------------------------------------------------------------|| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *cos|----------------------------------------------------------------| | \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *sin|----------------------------------------------------------------|| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *cos|----------------------------------------------------------------|
3*re(x) |3*im(x) \ 2 /| \ 2 / 3*re(x) |3*im(x) \ 2 /| \ 2 /
------- + I*|------- - --------------------------------------------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------------------------------------------- + ------- + I*|------- + --------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------
8 \ 8 8 / 8 8 \ 8 8 / 8
$$\left(i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{im}{\left(x\right)}}{8}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{re}{\left(x\right)}}{8}\right) + \left(i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{im}{\left(x\right)}}{8}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{re}{\left(x\right)}}{8}\right)$$
=
/ __________________________________________________________________ \ / __________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| | 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/||
| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *sin|----------------------------------------------------------------|| | \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *sin|----------------------------------------------------------------||
3*re(x) |3*im(x) \ 2 /| |3*im(x) \ 2 /|
------- + I*|------- - --------------------------------------------------------------------------------------------------------------------------------------------| + I*|------- + --------------------------------------------------------------------------------------------------------------------------------------------|
4 \ 8 8 / \ 8 8 /
$$i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{im}{\left(x\right)}}{8}\right) + i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{im}{\left(x\right)}}{8}\right) + \frac{3 \operatorname{re}{\left(x\right)}}{4}$$
producto
/ / __________________________________________________________________ \ __________________________________________________________________ \ / / __________________________________________________________________ \ __________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| | | 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| | | \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *sin|----------------------------------------------------------------|| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *cos|----------------------------------------------------------------|| | | \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *sin|----------------------------------------------------------------|| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *cos|----------------------------------------------------------------|| |3*re(x) |3*im(x) \ 2 /| \ 2 /| |3*re(x) |3*im(x) \ 2 /| \ 2 /| |------- + I*|------- - --------------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------------------------------------------------------------|*|------- + I*|------- + --------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------| \ 8 \ 8 8 / 8 / \ 8 \ 8 8 / 8 /
$$\left(i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{im}{\left(x\right)}}{8}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{re}{\left(x\right)}}{8}\right) \left(i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{im}{\left(x\right)}}{8}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{re}{\left(x\right)}}{8}\right)$$
=
2 2 3 3*re(x) im (x) re (x) 3*I*im(x) I*im(x)*re(x) - - - ------- - ------ + ------ - --------- + ------------- 2 8 8 8 8 4
$$\frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{8} + \frac{i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{4} - \frac{3 \operatorname{re}{\left(x\right)}}{8} - \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{8} - \frac{3 i \operatorname{im}{\left(x\right)}}{8} - \frac{3}{2}$$
-3/2 - 3*re(x)/8 - im(x)^2/8 + re(x)^2/8 - 3*i*im(x)/8 + i*im(x)*re(x)/4
Respuesta rápida
[src]
/ __________________________________________________________________ \ __________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|
| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *sin|----------------------------------------------------------------|| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *cos|----------------------------------------------------------------|
3*re(x) |3*im(x) \ 2 /| \ 2 /
y1 = ------- + I*|------- - --------------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------------------------------------------------------------
8 \ 8 8 / 8
$$y_{1} = i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{im}{\left(x\right)}}{8}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{re}{\left(x\right)}}{8}$$
/ __________________________________________________________________ \ __________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|| 4 / 2 / 2 2 \ |atan2\24*im(x) + 2*im(x)*re(x), 96 + re (x) - im (x) + 24*re(x)/|
| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *sin|----------------------------------------------------------------|| \/ (24*im(x) + 2*im(x)*re(x)) + \96 + re (x) - im (x) + 24*re(x)/ *cos|----------------------------------------------------------------|
3*re(x) |3*im(x) \ 2 /| \ 2 /
y2 = ------- + I*|------- + --------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------
8 \ 8 8 / 8
$$y_{2} = i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{im}{\left(x\right)}}{8}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 24 \operatorname{im}{\left(x\right)},\left(\operatorname{re}{\left(x\right)}\right)^{2} + 24 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} + 96 \right)}}{2} \right)}}{8} + \frac{3 \operatorname{re}{\left(x\right)}}{8}$$
y2 = i*(((2*re(x)*im(x) + 24*im(x))^2 + (re(x)^2 + 24*re(x) - im(x)^2 + 96)^2)^(1/4)*sin(atan2(2*re(x)*im(x) + 24*im(x, re(x)^2 + 24*re(x) - im(x)^2 + 96)/2)/8 + 3*im(x)/8) + ((2*re(x)*im(x) + 24*im(x))^2 + (re(x)^2 + 24*re(x) - im(x)^2 + 96)^2)^(1/4)*cos(atan2(2*re(x)*im(x) + 24*im(x), re(x)^2 + 24*re(x) - im(x)^2 + 96)/2)/8 + 3*re(x)/8)