Sr Examen
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- La ecuación:
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Ecuación 8*x=2
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Ecuación 3^x=81
-
Ecuación 5x+15=x-1
-
Ecuación 2*x^2-x+5=0
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -17*x+2*y=9
-
Expresiones idénticas
- (y^ dos)/ dos +y=Const-(x^ dos)/ dos
- (y al cuadrado ) dividir por 2 más y es igual a Const menos (x al cuadrado ) dividir por 2
- (y en el grado dos) dividir por dos más y es igual a Const menos (x en el grado dos) dividir por dos
- (y2)/2+y=Const-(x2)/2
- y2/2+y=Const-x2/2
- (y²)/2+y=Const-(x²)/2
- (y en el grado 2)/2+y=Const-(x en el grado 2)/2
- y^2/2+y=Const-x^2/2
- (y^2) dividir por 2+y=Const-(x^2) dividir por 2
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Expresiones semejantes
- (y^2)/2-y=Const-(x^2)/2
- (y^2)/2+y=Const+(x^2)/2
(y^2)/2+y=Const-(x^2)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\frac{y^{2}}{2} + y = c - \frac{x^{2}}{2}$$
en
$$\left(- c + \frac{x^{2}}{2}\right) + \left(\frac{y^{2}}{2} + y\right) = 0$$
Abramos la expresión en la ecuación
$$\left(- c + \frac{x^{2}}{2}\right) + \left(\frac{y^{2}}{2} + y\right) = 0$$
Obtenemos la ecuación cuadrática
$$- c + \frac{x^{2}}{2} + \frac{y^{2}}{2} + y = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \frac{1}{2}$$
$$b = 0$$
$$c = - c + \frac{y^{2}}{2} + y$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \sqrt{2 c - y^{2} - 2 y}$$
$$x_{2} = - \sqrt{2 c - y^{2} - 2 y}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\frac{y^{2}}{2} + y = c - \frac{x^{2}}{2}$$
en
$$\left(- c + \frac{x^{2}}{2}\right) + \left(\frac{y^{2}}{2} + y\right) = 0$$
Abramos la expresión en la ecuación
$$\left(- c + \frac{x^{2}}{2}\right) + \left(\frac{y^{2}}{2} + y\right) = 0$$
Obtenemos la ecuación cuadrática
$$- c + \frac{x^{2}}{2} + \frac{y^{2}}{2} + y = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \frac{1}{2}$$
$$b = 0$$
$$c = - c + \frac{y^{2}}{2} + y$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1/2) * (y + y^2/2 - c) = -y^2 - 2*y + 2*c
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \sqrt{2 c - y^{2} - 2 y}$$
$$x_{2} = - \sqrt{2 c - y^{2} - 2 y}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\frac{y^{2}}{2} + y = c - \frac{x^{2}}{2}$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- 2 c + x^{2} + y^{2} + 2 y = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - 2 c + y^{2} + 2 y$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - 2 c + y^{2} + 2 y$$
$$\frac{y^{2}}{2} + y = c - \frac{x^{2}}{2}$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- 2 c + x^{2} + y^{2} + 2 y = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - 2 c + y^{2} + 2 y$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - 2 c + y^{2} + 2 y$$
Gráfica
Suma y producto de raíces
[src]
suma
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/| 4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/| 4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/| 4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/|
- \/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *cos|------------------------------------------------------------------------------| - I*\/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *sin|------------------------------------------------------------------------------| + \/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *cos|------------------------------------------------------------------------------| + I*\/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *sin|------------------------------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ ________________________________________________________________________________ ________________________________________________________________________________ \ / ________________________________________________________________________________ ________________________________________________________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/| 4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/|| |4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/| 4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/|| |- \/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *cos|------------------------------------------------------------------------------| - I*\/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *sin|------------------------------------------------------------------------------||*|\/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *cos|------------------------------------------------------------------------------| + I*\/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *sin|------------------------------------------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
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/ 2 / 2 2 \
/ / 2 2 \ 2 I*atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/
-\/ \im (y) - re (y) - 2*re(y) + 2*re(c)/ + 4*(-im(c) + im(y)*re(y) + im(y)) *e
$$- \sqrt{4 \left(\operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}$$
-sqrt((im(y)^2 - re(y)^2 - 2*re(y) + 2*re(c))^2 + 4*(-im(c) + im(y)*re(y) + im(y))^2)*exp(i*atan2(-2*im(y) + 2*im(c) - 2*im(y)*re(y), im(y)^2 - re(y)^2 - 2*re(y) + 2*re(c)))
Respuesta rápida
[src]
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/| 4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/|
x1 = - \/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *cos|------------------------------------------------------------------------------| - I*\/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *sin|------------------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}$$
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/| 4 / 2 / 2 2 \ |atan2\-2*im(y) + 2*im(c) - 2*im(y)*re(y), im (y) - re (y) - 2*re(y) + 2*re(c)/|
x2 = \/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *cos|------------------------------------------------------------------------------| + I*\/ (-2*im(y) + 2*im(c) - 2*im(y)*re(y)) + \im (y) - re (y) - 2*re(y) + 2*re(c)/ *sin|------------------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(c\right)} - 2 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(c\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}$$
x2 = i*((-2*re(y)*im(y) + 2*im(c) - 2*im(y))^2 + (2*re(c) - re(y)^2 - 2*re(y) + im(y)^2)^2)^(1/4)*sin(atan2(-2*re(y)*im(y) + 2*im(c) - 2*im(y, 2*re(c) - re(y)^2 - 2*re(y) + im(y)^2)/2) + ((-2*re(y)*im(y) + 2*im(c) - 2*im(y))^2 + (2*re(c) - re(y)^2 - 2*re(y) + im(y)^2)^2)^(1/4)*cos(atan2(-2*re(y)*im(y) + 2*im(c) - 2*im(y), 2*re(c) - re(y)^2 - 2*re(y) + im(y)^2)/2))