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y=sqrt((a-3)*x^2-(6-2*a)*x+5) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
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y = \/ (a - 3)*x - (6 - 2*a)*x + 5
$$y = \sqrt{\left(x^{2} \left(a - 3\right) - x \left(6 - 2 a\right)\right) + 5}$$
Solución detallada
Tenemos la ecuación
$$y = \sqrt{\left(x^{2} \left(a - 3\right) - x \left(6 - 2 a\right)\right) + 5}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \sqrt{x^{2} \left(a - 3\right) + x \left(2 a - 6\right) + 5} = - y$$
Elevemos las dos partes de la ecuación a la potencia 2
$$x^{2} \left(a - 3\right) + x \left(2 a - 6\right) + 5 = y^{2}$$
$$x^{2} \left(a - 3\right) + x \left(2 a - 6\right) + 5 = y^{2}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$x^{2} \left(a - 3\right) + x \left(2 a - 6\right) - y^{2} + 5 = 0$$
Abramos la expresión en la ecuación
$$x^{2} \left(a - 3\right) + x \left(2 a - 6\right) - y^{2} + 5 = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} + 2 a x - 3 x^{2} - 6 x - y^{2} + 5 = 0$$
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
$$b = 2 a - 6$$
$$c = 5 - y^{2}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{- 2 a + \sqrt{- \left(5 - y^{2}\right) \left(4 a - 12\right) + \left(2 a - 6\right)^{2}} + 6}{2 a - 6}$$
$$x_{2} = \frac{- 2 a - \sqrt{- \left(5 - y^{2}\right) \left(4 a - 12\right) + \left(2 a - 6\right)^{2}} + 6}{2 a - 6}$$
$$y = \sqrt{\left(x^{2} \left(a - 3\right) - x \left(6 - 2 a\right)\right) + 5}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \sqrt{x^{2} \left(a - 3\right) + x \left(2 a - 6\right) + 5} = - y$$
Elevemos las dos partes de la ecuación a la potencia 2
$$x^{2} \left(a - 3\right) + x \left(2 a - 6\right) + 5 = y^{2}$$
$$x^{2} \left(a - 3\right) + x \left(2 a - 6\right) + 5 = y^{2}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$x^{2} \left(a - 3\right) + x \left(2 a - 6\right) - y^{2} + 5 = 0$$
Abramos la expresión en la ecuación
$$x^{2} \left(a - 3\right) + x \left(2 a - 6\right) - y^{2} + 5 = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} + 2 a x - 3 x^{2} - 6 x - y^{2} + 5 = 0$$
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
False
$$b = 2 a - 6$$
$$c = 5 - y^{2}$$
, entonces
D = b^2 - 4 * a * c =
(-6 + 2*a)^2 - 4 * (-3 + a) * (5 - y^2) = (-6 + 2*a)^2 - (-12 + 4*a)*(5 - y^2)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{- 2 a + \sqrt{- \left(5 - y^{2}\right) \left(4 a - 12\right) + \left(2 a - 6\right)^{2}} + 6}{2 a - 6}$$
$$x_{2} = \frac{- 2 a - \sqrt{- \left(5 - y^{2}\right) \left(4 a - 12\right) + \left(2 a - 6\right)^{2}} + 6}{2 a - 6}$$
Gráfica
Respuesta rápida
[src]
/ / _______________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________ \ \ / _______________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________ \
| | / 2 2 / / / 2\ 2 2 2 2 / 2\\\| | / 2 2 / / / 2\ 2 2 2 2 / 2\\\| | | / 2 2 / / / 2\ 2 2 2 2 / 2\\\| | / 2 2 / / / 2\ 2 2 2 2 / 2\\\|
| | 4 / / / 2\\ / 2 2 2 2 / 2\\ |atan2\-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y /, 24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y //|| | 4 / / / 2\\ / 2 2 2 2 / 2\\ |atan2\-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y /, 24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y //|| | | 4 / / / 2\\ / 2 2 2 2 / 2\\ |atan2\-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y /, 24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y //|| | 4 / / / 2\\ / 2 2 2 2 / 2\\ |atan2\-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y /, 24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y //||
|(-3 + re(a))*|-im(a) - \/ \-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y // + \24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y // *sin|-----------------------------------------------------------------------------------------------------------------------------|| |3 - re(a) - \/ \-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y // + \24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y // *cos|-----------------------------------------------------------------------------------------------------------------------------||*im(a)| (-3 + re(a))*|3 - re(a) - \/ \-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y // + \24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y // *cos|-----------------------------------------------------------------------------------------------------------------------------|| |-im(a) - \/ \-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y // + \24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y // *sin|-----------------------------------------------------------------------------------------------------------------------------||*im(a)
| \ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 //
x1 = I*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ (-3 + re(a)) + im (a) (-3 + re(a)) + im (a) / (-3 + re(a)) + im (a) (-3 + re(a)) + im (a)
$$x_{1} = \frac{\left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 3\right)}{\left(\operatorname{re}{\left(a\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 3\right) \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
/ / _______________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________ \ \ / _______________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________ \
| | / 2 2 / / / 2\ 2 2 2 2 / 2\\\| | / 2 2 / / / 2\ 2 2 2 2 / 2\\\| | | / 2 2 / / / 2\ 2 2 2 2 / 2\\\| | / 2 2 / / / 2\ 2 2 2 2 / 2\\\|
| | 4 / / / 2\\ / 2 2 2 2 / 2\\ |atan2\-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y /, 24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y //|| | 4 / / / 2\\ / 2 2 2 2 / 2\\ |atan2\-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y /, 24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y //|| | | 4 / / / 2\\ / 2 2 2 2 / 2\\ |atan2\-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y /, 24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y //|| | 4 / / / 2\\ / 2 2 2 2 / 2\\ |atan2\-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y /, 24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y //||
|(-3 + re(a))*|-im(a) + \/ \-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y // + \24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y // *sin|-----------------------------------------------------------------------------------------------------------------------------|| |3 - re(a) + \/ \-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y // + \24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y // *cos|-----------------------------------------------------------------------------------------------------------------------------||*im(a)| (-3 + re(a))*|3 - re(a) + \/ \-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y // + \24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y // *cos|-----------------------------------------------------------------------------------------------------------------------------|| |-im(a) + \/ \-11*im(a) - 6*im(y)*re(y) + 2*im(a)*re(a) + im\a*y // + \24 + re (a) - im (a) - 11*re(a) - 3*re (y) + 3*im (y) + re\a*y // *sin|-----------------------------------------------------------------------------------------------------------------------------||*im(a)
| \ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 //
x2 = I*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ (-3 + re(a)) + im (a) (-3 + re(a)) + im (a) / (-3 + re(a)) + im (a) (-3 + re(a)) + im (a)
$$x_{2} = \frac{\left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 3\right)}{\left(\operatorname{re}{\left(a\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 3\right) \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 11 \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(a y^{2}\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 11 \operatorname{re}{\left(a\right)} - 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(a y^{2}\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 24 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x2 = (((2*re(a)*im(a) - 6*re(y)*im(y) - 11*im(a) + im(a*y^2))^2 + (re(a)^2 - 11*re(a) - 3*re(y)^2 + re(a*y^2) - im(a)^2 + 3*im(y)^2 + 24)^2)^(1/4)*sin(atan2(2*re(a)*im(a) - 6*re(y)*im(y) - 11*im(a) + im(a*y^2, re(a)^2 - 11*re(a) - 3*re(y)^2 + re(a*y^2) - im(a)^2 + 3*im(y)^2 + 24)/2) - im(a))*im(a)/((re(a) - 3)^2 + im(a)^2) + i*((((2*re(a)*im(a) - 6*re(y)*im(y) - 11*im(a) + im(a*y^2))^2 + (re(a)^2 - 11*re(a) - 3*re(y)^2 + re(a*y^2) - im(a)^2 + 3*im(y)^2 + 24)^2)^(1/4)*sin(atan2(2*re(a)*im(a) - 6*re(y)*im(y) - 11*im(a) + im(a*y^2), re(a)^2 - 11*re(a) - 3*re(y)^2 + re(a*y^2) - im(a)^2 + 3*im(y)^2 + 24)/2) - im(a))*(re(a) - 3)/((re(a) - 3)^2 + im(a)^2) - (((2*re(a)*im(a) - 6*re(y)*im(y) - 11*im(a) + im(a*y^2))^2 + (re(a)^2 - 11*re(a) - 3*re(y)^2 + re(a*y^2) - im(a)^2 + 3*im(y)^2 + 24)^2)^(1/4)*cos(atan2(2*re(a)*im(a) - 6*re(y)*im(y) - 11*im(a) + im(a*y^2), re(a)^2 - 11*re(a) - 3*re(y)^2 + re(a*y^2) - im(a)^2 + 3*im(y)^2 + 24)/2) - re(a) + 3)*im(a)/((re(a) - 3)^2 + im(a)^2)) + (re(a) - 3)*(((2*re(a)*im(a) - 6*re(y)*im(y) - 11*im(a) + im(a*y^2))^2 + (re(a)^2 - 11*re(a) - 3*re(y)^2 + re(a*y^2) - im(a)^2 + 3*im(y)^2 + 24)^2)^(1/4)*cos(atan2(2*re(a)*im(a) - 6*re(y)*im(y) - 11*im(a) + im(a*y^2), re(a)^2 - 11*re(a) - 3*re(y)^2 + re(a*y^2) - im(a)^2 + 3*im(y)^2 + 24)/2) - re(a) + 3)/((re(a) - 3)^2 + im(a)^2))