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(3/(x+y-1))+(1/(2*x-y+3))+(7/5)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
    3            1        7    
--------- + ----------- + - = 0
x + y - 1   2*x - y + 3   5    
$$\left(\frac{1}{\left(2 x - y\right) + 3} + \frac{3}{\left(x + y\right) - 1}\right) + \frac{7}{5} = 0$$
Solución detallada
Tenemos la ecuación:
$$\left(\frac{1}{\left(2 x - y\right) + 3} + \frac{3}{\left(x + y\right) - 1}\right) + \frac{7}{5} = 0$$
Multipliquemos las dos partes de la ecuación por los denominadores:
-1 + x + y y 3 - y + 2*x
obtendremos:
$$\left(\left(\frac{1}{\left(2 x - y\right) + 3} + \frac{3}{\left(x + y\right) - 1}\right) + \frac{7}{5}\right) \left(x + y - 1\right) = 0$$
$$\frac{35 x - 10 y + 7 \left(x + y - 1\right) \left(2 x - y + 3\right) + 40}{5 \left(2 x - y + 3\right)} = 0$$
$$\frac{35 x - 10 y + 7 \left(x + y - 1\right) \left(2 x - y + 3\right) + 40}{5 \left(2 x - y + 3\right)} \left(2 x - y + 3\right) = 0 \left(2 x - y + 3\right)$$
$$\frac{14 x^{2}}{5} + \frac{7 x y}{5} + \frac{42 x}{5} - \frac{7 y^{2}}{5} + \frac{18 y}{5} + \frac{19}{5} = 0$$
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
$$a = \frac{14}{5}$$
$$b = \frac{7 y}{5} + \frac{42}{5}$$
$$c = - \frac{7 y^{2}}{5} + \frac{18 y}{5} + \frac{19}{5}$$
, entonces
D = b^2 - 4 * a * c = 

(42/5 + 7*y/5)^2 - 4 * (14/5) * (19/5 - 7*y^2/5 + 18*y/5) = -1064/25 + (42/5 + 7*y/5)^2 - 1008*y/25 + 392*y^2/25

La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

o
$$x_{1} = - \frac{y}{4} + \frac{5 \sqrt{\frac{392 y^{2}}{25} - \frac{1008 y}{25} + \left(\frac{7 y}{5} + \frac{42}{5}\right)^{2} - \frac{1064}{25}}}{28} - \frac{3}{2}$$
$$x_{2} = - \frac{y}{4} - \frac{5 \sqrt{\frac{392 y^{2}}{25} - \frac{1008 y}{25} + \left(\frac{7 y}{5} + \frac{42}{5}\right)^{2} - \frac{1064}{25}}}{28} - \frac{3}{2}$$
Gráfica
Respuesta rápida [src]
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                     |             /                                                                              2     /     /                                          2                        2   \\|      /                                                                              2     /     /                                          2                        2   \\
                     |          4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||   4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|
                     |          \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *sin|------------------------------------------------------------------------------||   \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *cos|------------------------------------------------------------------------------|
       3   re(y)     |  im(y)                                                                                           \                                      2                                       /|                                                                                           \                                      2                                       /
x1 = - - - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       2     4       \    4                                                                                        28                                                                                   /                                                                                      28                                                                                   
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}$$
                     /              ________________________________________________________________________________                                                                                    \       ________________________________________________________________________________                                                                                    
                     |             /                                                                              2     /     /                                          2                        2   \\|      /                                                                              2     /     /                                          2                        2   \\
                     |          4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||   4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|
                     |          \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *sin|------------------------------------------------------------------------------||   \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *cos|------------------------------------------------------------------------------|
       3   re(y)     |  im(y)                                                                                           \                                      2                                       /|                                                                                           \                                      2                                       /
x2 = - - - ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       2     4       \    4                                                                                        28                                                                                   /                                                                                      28                                                                                   
$$x_{2} = i \left(\frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}$$
x2 = i*(((882*re(y)*im(y) - 420*im(y))^2 + (441*re(y)^2 - 420*re(y) - 441*im(y)^2 + 700)^2)^(1/4)*sin(atan2(882*re(y)*im(y) - 420*im(y, 441*re(y)^2 - 420*re(y) - 441*im(y)^2 + 700)/2)/28 - im(y)/4) + ((882*re(y)*im(y) - 420*im(y))^2 + (441*re(y)^2 - 420*re(y) - 441*im(y)^2 + 700)^2)^(1/4)*cos(atan2(882*re(y)*im(y) - 420*im(y), 441*re(y)^2 - 420*re(y) - 441*im(y)^2 + 700)/2)/28 - re(y)/4 - 3/2)
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\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||   4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|                   |          4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||   4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|
                |          \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *sin|------------------------------------------------------------------------------||   \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *cos|------------------------------------------------------------------------------|                   |          \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *sin|------------------------------------------------------------------------------||   \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *cos|------------------------------------------------------------------------------|
  3   re(y)     |  im(y)                                                                                           \                                      2                                       /|                                                                                           \                                      2                                       /     3   re(y)     |  im(y)                                                                                           \                                      2                                       /|                                                                                           \                                      2                                       /
- - - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + - - - ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  2     4       \    4                                                                                        28                                                                                   /                                                                                      28                                                                                        2     4       \    4                                                                                        28                                                                                   /                                                                                      28                                                                                   
$$\left(i \left(- \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}\right) + \left(i \left(\frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}\right)$$
=
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               |             /                                                                              2     /     /                                          2                        2   \\|     |             /                                                                              2     /     /                                          2                        2   \\|
               |          4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||     |          4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||
               |          \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *sin|------------------------------------------------------------------------------||     |          \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *sin|------------------------------------------------------------------------------||
     re(y)     |  im(y)                                                                                           \                                      2                                       /|     |  im(y)                                                                                           \                                      2                                       /|
-3 - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
       2       \    4                                                                                        28                                                                                   /     \    4                                                                                        28                                                                                   /
$$i \left(- \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) + i \left(\frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} - 3$$
producto
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|                |             /                                                                              2     /     /                                          2                        2   \\|      /                                                                              2     /     /                                          2                        2   \\| |                |             /                                                                              2     /     /                                          2                        2   \\|      /                                                                              2     /     /                                          2                        2   \\|
|                |          4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||   4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/|| |                |          4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||   4 /                                2   /            2                        2   \      |atan2\-420*im(y) + 882*im(y)*re(y), 700 - 441*im (y) - 420*re(y) + 441*re (y)/||
|                |          \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *sin|------------------------------------------------------------------------------||   \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *cos|------------------------------------------------------------------------------|| |                |          \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *sin|------------------------------------------------------------------------------||   \/   (-420*im(y) + 882*im(y)*re(y))  + \700 - 441*im (y) - 420*re(y) + 441*re (y)/  *cos|------------------------------------------------------------------------------||
|  3   re(y)     |  im(y)                                                                                           \                                      2                                       /|                                                                                           \                                      2                                       /| |  3   re(y)     |  im(y)                                                                                           \                                      2                                       /|                                                                                           \                                      2                                       /|
|- - - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- - - ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\  2     4       \    4                                                                                        28                                                                                   /                                                                                      28                                                                                   / \  2     4       \    4                                                                                        28                                                                                   /                                                                                      28                                                                                   /
$$\left(i \left(- \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}\right) \left(i \left(\frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)}\right)^{2} + \left(441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(882 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 420 \operatorname{im}{\left(y\right)},441 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 420 \operatorname{re}{\left(y\right)} - 441 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 700 \right)}}{2} \right)}}{28} - \frac{\operatorname{re}{\left(y\right)}}{4} - \frac{3}{2}\right)$$
=
       2        2                                         
19   im (y)   re (y)   9*re(y)   9*I*im(y)                
-- + ------ - ------ + ------- + --------- - I*im(y)*re(y)
14     2        2         7          7                    
$$- \frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{2} - i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \frac{9 \operatorname{re}{\left(y\right)}}{7} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{2} + \frac{9 i \operatorname{im}{\left(y\right)}}{7} + \frac{19}{14}$$
19/14 + im(y)^2/2 - re(y)^2/2 + 9*re(y)/7 + 9*i*im(y)/7 - i*im(y)*re(y)