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y=1/2•x^2+(а-10)x+а la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2                 
    x                  
y = -- + (a - 10)*x + a
    2
y=a+(x22+x(a−10))y = a + \left(\frac{x^{2}}{2} + x \left(a - 10\right)\right)
Simplificar
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.

La ecuación se convierte de
y=a+(x22+x(a−10))y = a + \left(\frac{x^{2}}{2} + x \left(a - 10\right)\right)
en
y+(−a+(−x22−x(a−10)))=0y + \left(- a + \left(- \frac{x^{2}}{2} - x \left(a - 10\right)\right)\right) = 0
Abramos la expresión en la ecuación
y+(−a+(−x22−x(a−10)))=0y + \left(- a + \left(- \frac{x^{2}}{2} - x \left(a - 10\right)\right)\right) = 0
Obtenemos la ecuación cuadrática
−ax−a−x22+10x+y=0- a x - a - \frac{x^{2}}{2} + 10 x + y = 0
Es la ecuación de la forma
a*x^2 + b*x + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=−12a = - \frac{1}{2}
b=10−ab = 10 - a
c=−a+yc = - a + y
, entonces
D = b^2 - 4 * a * c = 

(10 - a)^2 - 4 * (-1/2) * (y - a) = (10 - a)^2 - 2*a + 2*y

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

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

o
x1=−a−−2a+2y+(10−a)2+10x_{1} = - a - \sqrt{- 2 a + 2 y + \left(10 - a\right)^{2}} + 10
x2=−a+−2a+2y+(10−a)2+10x_{2} = - a + \sqrt{- 2 a + 2 y + \left(10 - a\right)^{2}} + 10
Teorema de Cardano-Vieta
reescribamos la ecuación
y=a+(x22+x(a−10))y = a + \left(\frac{x^{2}}{2} + x \left(a - 10\right)\right)
de
ax2+bx+c=0a x^{2} + b x + c = 0
como ecuación cuadrática reducida
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
2a+x2+2x(a−10)−2y=02 a + x^{2} + 2 x \left(a - 10\right) - 2 y = 0
px+q+x2=0p x + q + x^{2} = 0
donde
p=bap = \frac{b}{a}
p=2a−20p = 2 a - 20
q=caq = \frac{c}{a}
q=2a−2yq = 2 a - 2 y
Fórmulas de Cardano-Vieta
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=20−2ax_{1} + x_{2} = 20 - 2 a
x1x2=2a−2yx_{1} x_{2} = 2 a - 2 y
Gráfica
Respuesta rápida [src] 
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                    |            /                                                                                      2     /     /                                             2        2                        \\|      /                                                                                      2     /     /                                             2        2                        \\
                    |         4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||   4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/|
x1 = 10 - re(a) + I*|-im(a) - \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *sin|--------------------------------------------------------------------------------------|| - \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *cos|--------------------------------------------------------------------------------------|
                    \                                                                                                         \                                          2                                           //                                                                                                   \                                          2                                           /
x1=i(−(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−im⁡(a))−(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−re⁡(a)+10x_{1} = i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 10 
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                    |            /                                                                                      2     /     /                                             2        2                        \\|      /                                                                                      2     /     /                                             2        2                        \\
                    |         4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||   4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/|
x2 = 10 - re(a) + I*|-im(a) + \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *sin|--------------------------------------------------------------------------------------|| + \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *cos|--------------------------------------------------------------------------------------|
                    \                                                                                                         \                                          2                                           //                                                                                                   \                                          2                                           /
x2=i((2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−im⁡(a))+(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−re⁡(a)+10x_{2} = i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 10 
x2 = i*(((2*re(a)*im(a) - 22*im(a) + 2*im(y))^2 + (re(a)^2 - 22*re(a) + 2*re(y) - im(a)^2 + 100)^2)^(1/4)*sin(atan2(2*re(a)*im(a) - 22*im(a) + 2*im(y, re(a)^2 - 22*re(a) + 2*re(y) - im(a)^2 + 100)/2) - im(a)) + ((2*re(a)*im(a) - 22*im(a) + 2*im(y))^2 + (re(a)^2 - 22*re(a) + 2*re(y) - im(a)^2 + 100)^2)^(1/4)*cos(atan2(2*re(a)*im(a) - 22*im(a) + 2*im(y), re(a)^2 - 22*re(a) + 2*re(y) - im(a)^2 + 100)/2) - re(a) + 10)
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\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||   4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/|                  |         4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||   4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/|
10 - re(a) + I*|-im(a) - \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *sin|--------------------------------------------------------------------------------------|| - \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *cos|--------------------------------------------------------------------------------------| + 10 - re(a) + I*|-im(a) + \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *sin|--------------------------------------------------------------------------------------|| + \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *cos|--------------------------------------------------------------------------------------|
               \                                                                                                         \                                          2                                           //                                                                                                   \                                          2                                           /                  \                                                                                                         \                                          2                                           //                                                                                                   \                                          2                                           /
(i(−(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−im⁡(a))−(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−re⁡(a)+10)+(i((2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−im⁡(a))+(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−re⁡(a)+10)\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 10\right) + \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 10\right) 
=
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                 |            /                                                                                      2     /     /                                             2        2                        \\|     |            /                                                                                      2     /     /                                             2        2                        \\|
                 |         4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||     |         4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||
20 - 2*re(a) + I*|-im(a) + \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *sin|--------------------------------------------------------------------------------------|| + I*|-im(a) - \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *sin|--------------------------------------------------------------------------------------||
                 \                                                                                                         \                                          2                                           //     \                                                                                                         \                                          2                                           //
i(−(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−im⁡(a))+i((2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−im⁡(a))−2re⁡(a)+20i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) - 2 \operatorname{re}{\left(a\right)} + 20 
producto
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|               |            /                                                                                      2     /     /                                             2        2                        \\|      /                                                                                      2     /     /                                             2        2                        \\| |               |            /                                                                                      2     /     /                                             2        2                        \\|      /                                                                                      2     /     /                                             2        2                        \\|
|               |         4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||   4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/|| |               |         4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||   4 /                                       2   /        2        2                        \      |atan2\-22*im(a) + 2*im(y) + 2*im(a)*re(a), 100 + re (a) - im (a) - 22*re(a) + 2*re(y)/||
|10 - re(a) + I*|-im(a) - \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *sin|--------------------------------------------------------------------------------------|| - \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *cos|--------------------------------------------------------------------------------------||*|10 - re(a) + I*|-im(a) + \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *sin|--------------------------------------------------------------------------------------|| + \/   (-22*im(a) + 2*im(y) + 2*im(a)*re(a))  + \100 + re (a) - im (a) - 22*re(a) + 2*re(y)/  *cos|--------------------------------------------------------------------------------------||
\               \                                                                                                         \                                          2                                           //                                                                                                   \                                          2                                           // \               \                                                                                                         \                                          2                                           //                                                                                                   \                                          2                                           //
(i(−(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−im⁡(a))−(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−re⁡(a)+10)(i((2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−im⁡(a))+(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y))2+((re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−22im⁡(a)+2im⁡(y),(re⁡(a))2−22re⁡(a)+2re⁡(y)−(im⁡(a))2+100)2)−re⁡(a)+10)\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 10\right) \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 22 \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - 22 \operatorname{re}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 100 \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} + 10\right) 
=
-2*re(y) + 2*re(a) - 2*I*im(y) + 2*I*im(a)
2re⁡(a)−2re⁡(y)+2iim⁡(a)−2iim⁡(y)2 \operatorname{re}{\left(a\right)} - 2 \operatorname{re}{\left(y\right)} + 2 i \operatorname{im}{\left(a\right)} - 2 i \operatorname{im}{\left(y\right)} 
-2*re(y) + 2*re(a) - 2*i*im(y) + 2*i*im(a)
    © Sr Examen – Калькулятор