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- La ecuación:
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Ecuación 6*x^2+x-7=0
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Ecuación 2-5(3+2x)=17
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Ecuación (6*x+8)/2+5=5*x/3
- Expresar {x} en función de y en la ecuación:
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- 10*x+3*y=2
- 16*x-17*y=-15
- Integral de d{x}:
- x-y
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- x-y
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Expresiones idénticas
- (x-11y- ocho)/(3x-y- dieciséis)=x-y
- (x menos 11y menos 8) dividir por (3x menos y menos 16) es igual a x menos y
- (x menos 11y menos ocho) dividir por (3x menos y menos dieciséis) es igual a x menos y
- x-11y-8/3x-y-16=x-y
- (x-11y-8) dividir por (3x-y-16)=x-y
-
Expresiones semejantes
- (x+11y-8)/(3x-y-16)=x-y
- (x-11y-8)/(3x-y-16)=x+y
- (x-11y+8)/(3x-y-16)=x-y
- (x-11y-8)/(3x+y-16)=x-y
- (x-11y-8)/(3x-y+16)=x-y
(x-11y-8)/(3x-y-16)=x-y la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
x - 11*y - 8 ------------ = x - y 3*x - y - 16
$$\frac{\left(x - 11 y\right) - 8}{\left(3 x - y\right) - 16} = x - y$$
Solución detallada
Tenemos la ecuación:
$$\frac{\left(x - 11 y\right) - 8}{\left(3 x - y\right) - 16} = x - y$$
Multipliquemos las dos partes de la ecuación por los denominadores:
-16 - y + 3*x
obtendremos:
$$\frac{\left(\left(x - 11 y\right) - 8\right) \left(3 x - y - 16\right)}{\left(3 x - y\right) - 16} = \left(x - y\right) \left(3 x - y - 16\right)$$
$$x - 11 y - 8 = - \left(x - y\right) \left(- 3 x + y + 16\right)$$
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$x - 11 y - 8 = - \left(x - y\right) \left(- 3 x + y + 16\right)$$
en
$$- 3 x^{2} + 4 x y + 17 x - y^{2} - 27 y - 8 = 0$$
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
$$a = -3$$
$$b = 4 y + 17$$
$$c = - y^{2} - 27 y - 8$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{2 y}{3} - \frac{\sqrt{- 12 y^{2} - 324 y + \left(4 y + 17\right)^{2} - 96}}{6} + \frac{17}{6}$$
$$x_{2} = \frac{2 y}{3} + \frac{\sqrt{- 12 y^{2} - 324 y + \left(4 y + 17\right)^{2} - 96}}{6} + \frac{17}{6}$$
$$\frac{\left(x - 11 y\right) - 8}{\left(3 x - y\right) - 16} = x - y$$
Multipliquemos las dos partes de la ecuación por los denominadores:
-16 - y + 3*x
obtendremos:
$$\frac{\left(\left(x - 11 y\right) - 8\right) \left(3 x - y - 16\right)}{\left(3 x - y\right) - 16} = \left(x - y\right) \left(3 x - y - 16\right)$$
$$x - 11 y - 8 = - \left(x - y\right) \left(- 3 x + y + 16\right)$$
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$x - 11 y - 8 = - \left(x - y\right) \left(- 3 x + y + 16\right)$$
en
$$- 3 x^{2} + 4 x y + 17 x - y^{2} - 27 y - 8 = 0$$
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
$$a = -3$$
$$b = 4 y + 17$$
$$c = - y^{2} - 27 y - 8$$
, entonces
D = b^2 - 4 * a * c =
(17 + 4*y)^2 - 4 * (-3) * (-8 - y^2 - 27*y) = -96 + (17 + 4*y)^2 - 324*y - 12*y^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{2 y}{3} - \frac{\sqrt{- 12 y^{2} - 324 y + \left(4 y + 17\right)^{2} - 96}}{6} + \frac{17}{6}$$
$$x_{2} = \frac{2 y}{3} + \frac{\sqrt{- 12 y^{2} - 324 y + \left(4 y + 17\right)^{2} - 96}}{6} + \frac{17}{6}$$
Gráfica
Respuesta rápida
[src]
/ __________________________________________________________________________ \ __________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|
| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *sin|------------------------------------------------------------------------|| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *cos|------------------------------------------------------------------------|
17 2*re(y) |2*im(y) \ 2 /| \ 2 /
x1 = -- + ------- + I*|------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------
6 3 \ 3 6 / 6
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{im}{\left(y\right)}}{3}\right) - \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{re}{\left(y\right)}}{3} + \frac{17}{6}$$
/ __________________________________________________________________________ \ __________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|
| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *sin|------------------------------------------------------------------------|| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *cos|------------------------------------------------------------------------|
17 2*re(y) |2*im(y) \ 2 /| \ 2 /
x2 = -- + ------- + I*|------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------
6 3 \ 3 6 / 6
$$x_{2} = i \left(\frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{im}{\left(y\right)}}{3}\right) + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{re}{\left(y\right)}}{3} + \frac{17}{6}$$
x2 = i*(((8*re(y)*im(y) - 188*im(y))^2 + (4*re(y)^2 - 188*re(y) - 4*im(y)^2 + 193)^2)^(1/4)*sin(atan2(8*re(y)*im(y) - 188*im(y, 4*re(y)^2 - 188*re(y) - 4*im(y)^2 + 193)/2)/6 + 2*im(y)/3) + ((8*re(y)*im(y) - 188*im(y))^2 + (4*re(y)^2 - 188*re(y) - 4*im(y)^2 + 193)^2)^(1/4)*cos(atan2(8*re(y)*im(y) - 188*im(y), 4*re(y)^2 - 188*re(y) - 4*im(y)^2 + 193)/2)/6 + 2*re(y)/3 + 17/6)
Suma y producto de raíces
[src]
suma
/ __________________________________________________________________________ \ __________________________________________________________________________ / __________________________________________________________________________ \ __________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/| | 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|
| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *sin|------------------------------------------------------------------------|| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *cos|------------------------------------------------------------------------| | \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *sin|------------------------------------------------------------------------|| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *cos|------------------------------------------------------------------------|
17 2*re(y) |2*im(y) \ 2 /| \ 2 / 17 2*re(y) |2*im(y) \ 2 /| \ 2 /
-- + ------- + I*|------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------ + -- + ------- + I*|------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------
6 3 \ 3 6 / 6 6 3 \ 3 6 / 6
$$\left(i \left(- \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{im}{\left(y\right)}}{3}\right) - \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{re}{\left(y\right)}}{3} + \frac{17}{6}\right) + \left(i \left(\frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{im}{\left(y\right)}}{3}\right) + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{re}{\left(y\right)}}{3} + \frac{17}{6}\right)$$
=
/ __________________________________________________________________________ \ / __________________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| | 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/||
| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *sin|------------------------------------------------------------------------|| | \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *sin|------------------------------------------------------------------------||
17 4*re(y) |2*im(y) \ 2 /| |2*im(y) \ 2 /|
-- + ------- + I*|------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------|
3 3 \ 3 6 / \ 3 6 /
$$i \left(- \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{im}{\left(y\right)}}{3}\right) + i \left(\frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{im}{\left(y\right)}}{3}\right) + \frac{4 \operatorname{re}{\left(y\right)}}{3} + \frac{17}{3}$$
producto
/ / __________________________________________________________________________ \ __________________________________________________________________________ \ / / __________________________________________________________________________ \ __________________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| | | 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-188*im(y) + 8*im(y)*re(y), 193 - 188*re(y) - 4*im (y) + 4*re (y)/|| | | \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *sin|------------------------------------------------------------------------|| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *cos|------------------------------------------------------------------------|| | | \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *sin|------------------------------------------------------------------------|| \/ (-188*im(y) + 8*im(y)*re(y)) + \193 - 188*re(y) - 4*im (y) + 4*re (y)/ *cos|------------------------------------------------------------------------|| |17 2*re(y) |2*im(y) \ 2 /| \ 2 /| |17 2*re(y) |2*im(y) \ 2 /| \ 2 /| |-- + ------- + I*|------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- + ------- + I*|------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------| \6 3 \ 3 6 / 6 / \6 3 \ 3 6 / 6 /
$$\left(i \left(- \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{im}{\left(y\right)}}{3}\right) - \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{re}{\left(y\right)}}{3} + \frac{17}{6}\right) \left(i \left(\frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{im}{\left(y\right)}}{3}\right) + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 188 \operatorname{im}{\left(y\right)},4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 188 \operatorname{re}{\left(y\right)} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 193 \right)}}{2} \right)}}{6} + \frac{2 \operatorname{re}{\left(y\right)}}{3} + \frac{17}{6}\right)$$
=
2 2 8 im (y) re (y) 2*I*im(y)*re(y) - + 9*re(y) - ------ + ------ + 9*I*im(y) + --------------- 3 3 3 3
$$\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{3} + \frac{2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{3} + 9 \operatorname{re}{\left(y\right)} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{3} + 9 i \operatorname{im}{\left(y\right)} + \frac{8}{3}$$
8/3 + 9*re(y) - im(y)^2/3 + re(y)^2/3 + 9*i*im(y) + 2*i*im(y)*re(y)/3