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Expresiones semejantes
- 2*x^2-3*x*y-5*y=0
- 2*x^2+3*x*y+5*y=0
2*x^2-3*x*y+5*y=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 2$$
$$b = - 3 y$$
$$c = 5 y$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{3 y}{4} + \frac{\sqrt{9 y^{2} - 40 y}}{4}$$
$$x_{2} = \frac{3 y}{4} - \frac{\sqrt{9 y^{2} - 40 y}}{4}$$
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
$$a = 2$$
$$b = - 3 y$$
$$c = 5 y$$
, entonces
D = b^2 - 4 * a * c =
(-3*y)^2 - 4 * (2) * (5*y) = -40*y + 9*y^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{3 y}{4} + \frac{\sqrt{9 y^{2} - 40 y}}{4}$$
$$x_{2} = \frac{3 y}{4} - \frac{\sqrt{9 y^{2} - 40 y}}{4}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$5 y + \left(2 x^{2} - 3 x y\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{3 x y}{2} + \frac{5 y}{2} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{3 y}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{5 y}{2}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3 y}{2}$$
$$x_{1} x_{2} = \frac{5 y}{2}$$
$$5 y + \left(2 x^{2} - 3 x y\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{3 x y}{2} + \frac{5 y}{2} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{3 y}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{5 y}{2}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3 y}{2}$$
$$x_{1} x_{2} = \frac{5 y}{2}$$
Gráfica
Suma y producto de raíces
[src]
suma
/ __________________________________________________________________________________ \ __________________________________________________________________________________ / __________________________________________________________________________________ \ __________________________________________________________________________________
| / 2 / / 2 \\| / 2 / / 2 \\ | / 2 / / 2 \\| / 2 / / 2 \\
| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/| | 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|
| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *sin|--------------------------------------------------------------------------------|| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *cos|--------------------------------------------------------------------------------| | \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *sin|--------------------------------------------------------------------------------|| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *cos|--------------------------------------------------------------------------------|
3*re(y) |3*im(y) \ 2 /| \ 2 / 3*re(y) |3*im(y) \ 2 /| \ 2 /
------- + I*|------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------- + I*|------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 \ 4 4 / 4 4 \ 4 4 / 4
$$\left(i \left(- \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}\right) + \left(i \left(\frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}\right)$$
=
/ __________________________________________________________________________________ \ / __________________________________________________________________________________ \
| / 2 / / 2 \\| | / 2 / / 2 \\|
| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| | 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||
| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *sin|--------------------------------------------------------------------------------|| | \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *sin|--------------------------------------------------------------------------------||
3*re(y) |3*im(y) \ 2 /| |3*im(y) \ 2 /|
------- + I*|------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
2 \ 4 4 / \ 4 4 /
$$i \left(- \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + i \left(\frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{2}$$
producto
/ / __________________________________________________________________________________ \ __________________________________________________________________________________ \ / / __________________________________________________________________________________ \ __________________________________________________________________________________ \ | | / 2 / / 2 \\| / 2 / / 2 \\| | | / 2 / / 2 \\| / 2 / / 2 \\| | | 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| | | 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| | | \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *sin|--------------------------------------------------------------------------------|| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *cos|--------------------------------------------------------------------------------|| | | \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *sin|--------------------------------------------------------------------------------|| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *cos|--------------------------------------------------------------------------------|| |3*re(y) |3*im(y) \ 2 /| \ 2 /| |3*re(y) |3*im(y) \ 2 /| \ 2 /| |------- + I*|------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|------- + I*|------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 4 \ 4 4 / 4 / \ 4 \ 4 4 / 4 /
$$\left(i \left(- \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}\right) \left(i \left(\frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}\right)$$
=
5*re(y) 5*I*im(y) ------- + --------- 2 2
$$\frac{5 \operatorname{re}{\left(y\right)}}{2} + \frac{5 i \operatorname{im}{\left(y\right)}}{2}$$
5*re(y)/2 + 5*i*im(y)/2
Respuesta rápida
[src]
/ __________________________________________________________________________________ \ __________________________________________________________________________________
| / 2 / / 2 \\| / 2 / / 2 \\
| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|
| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *sin|--------------------------------------------------------------------------------|| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *cos|--------------------------------------------------------------------------------|
3*re(y) |3*im(y) \ 2 /| \ 2 /
x1 = ------- + I*|------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 \ 4 4 / 4
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}$$
/ __________________________________________________________________________________ \ __________________________________________________________________________________
| / 2 / / 2 \\| / 2 / / 2 \\
| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| 4 / / 2 \ 2 |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|
| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *sin|--------------------------------------------------------------------------------|| \/ \- 9*im (y) + (-40 + 9*re(y))*re(y)/ + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y)) *cos|--------------------------------------------------------------------------------|
3*re(y) |3*im(y) \ 2 /| \ 2 /
x2 = ------- + I*|------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 \ 4 4 / 4
$$x_{2} = i \left(\frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}$$
x2 = i*((((9*re(y) - 40)*re(y) - 9*im(y)^2)^2 + ((9*re(y) - 40)*im(y) + 9*re(y)*im(y))^2)^(1/4)*sin(atan2((9*re(y) - 40)*im(y) + 9*re(y)*im(y, (9*re(y) - 40)*re(y) - 9*im(y)^2)/2)/4 + 3*im(y)/4) + (((9*re(y) - 40)*re(y) - 9*im(y)^2)^2 + ((9*re(y) - 40)*im(y) + 9*re(y)*im(y))^2)^(1/4)*cos(atan2((9*re(y) - 40)*im(y) + 9*re(y)*im(y), (9*re(y) - 40)*re(y) - 9*im(y)^2)/2)/4 + 3*re(y)/4)