Sr Examen

Otras calculadoras

2*x^2-4*x*y-3y^2-16=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
   2              2         
2*x  - 4*x*y - 3*y  - 16 = 0
(−3y2+(2x2−4xy))−16=0\left(- 3 y^{2} + \left(2 x^{2} - 4 x y\right)\right) - 16 = 0
Simplificar
Solución detallada
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=2a = 2
b=−4yb = - 4 y
c=−3y2−16c = - 3 y^{2} - 16
, entonces
D = b^2 - 4 * a * c = 

(-4*y)^2 - 4 * (2) * (-16 - 3*y^2) = 128 + 40*y^2

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

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

o
x1=y+40y2+1284x_{1} = y + \frac{\sqrt{40 y^{2} + 128}}{4}
x2=y−40y2+1284x_{2} = y - \frac{\sqrt{40 y^{2} + 128}}{4}
Teorema de Cardano-Vieta
reescribamos la ecuación
(−3y2+(2x2−4xy))−16=0\left(- 3 y^{2} + \left(2 x^{2} - 4 x y\right)\right) - 16 = 0
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
x2−2xy−3y22−8=0x^{2} - 2 x y - \frac{3 y^{2}}{2} - 8 = 0
px+q+x2=0p x + q + x^{2} = 0
donde
p=bap = \frac{b}{a}
p=−2yp = - 2 y
q=caq = \frac{c}{a}
q=−3y22−8q = - \frac{3 y^{2}}{2} - 8
Fórmulas de Cardano-Vieta
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=2yx_{1} + x_{2} = 2 y
x1x2=−3y22−8x_{1} x_{2} = - \frac{3 y^{2}}{2} - 8
Gráfica
Suma y producto de raíces [src] 
suma
  /      ___________________________________________________                                                               \       ___________________________________________________                                                                    /    ___________________________________________________                                                               \       ___________________________________________________                                                               
  |     /                             2                         /     /                          2           2   \\        |      /                             2                         /     /                          2           2   \\             |   /                             2                         /     /                          2           2   \\        |      /                             2                         /     /                          2           2   \\        
  |  4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |   4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|             |4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |   4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        
  |  \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *sin|-------------------------------------------------|        |   \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *cos|-------------------------------------------------|             |\/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *sin|-------------------------------------------------|        |   \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *cos|-------------------------------------------------|        
  |                                                             \                        2                        /        |                                                              \                        2                        /             |                                                           \                        2                        /        |                                                              \                        2                        /        
I*|- -------------------------------------------------------------------------------------------------------------- + im(y)| - -------------------------------------------------------------------------------------------------------------- + re(y) + I*|-------------------------------------------------------------------------------------------------------------- + im(y)| + -------------------------------------------------------------------------------------------------------------- + re(y)
  \                                                        2                                                               /                                                         2                                                                    \                                                      2                                                               /                                                         2
(i(−(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+im⁡(y))−(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+re⁡(y))+(i((10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+im⁡(y))+(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+re⁡(y))\left(i \left(- \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{re}{\left(y\right)}\right) + \left(i \left(\frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{re}{\left(y\right)}\right) 
=
            /    ___________________________________________________                                                               \     /      ___________________________________________________                                                               \
            |   /                             2                         /     /                          2           2   \\        |     |     /                             2                         /     /                          2           2   \\        |
            |4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |     |  4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |
            |\/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *sin|-------------------------------------------------|        |     |  \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *sin|-------------------------------------------------|        |
            |                                                           \                        2                        /        |     |                                                             \                        2                        /        |
2*re(y) + I*|-------------------------------------------------------------------------------------------------------------- + im(y)| + I*|- -------------------------------------------------------------------------------------------------------------- + im(y)|
            \                                                      2                                                               /     \                                                        2                                                               /
i(−(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+im⁡(y))+i((10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+im⁡(y))+2re⁡(y)i \left(- \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)}\right) + i \left(\frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)}\right) + 2 \operatorname{re}{\left(y\right)} 
producto
/  /      ___________________________________________________                                                               \       ___________________________________________________                                                               \ /  /    ___________________________________________________                                                               \       ___________________________________________________                                                               \
|  |     /                             2                         /     /                          2           2   \\        |      /                             2                         /     /                          2           2   \\        | |  |   /                             2                         /     /                          2           2   \\        |      /                             2                         /     /                          2           2   \\        |
|  |  4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |   4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        | |  |4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |   4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |
|  |  \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *sin|-------------------------------------------------|        |   \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *cos|-------------------------------------------------|        | |  |\/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *sin|-------------------------------------------------|        |   \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *cos|-------------------------------------------------|        |
|  |                                                             \                        2                        /        |                                                              \                        2                        /        | |  |                                                           \                        2                        /        |                                                              \                        2                        /        |
|I*|- -------------------------------------------------------------------------------------------------------------- + im(y)| - -------------------------------------------------------------------------------------------------------------- + re(y)|*|I*|-------------------------------------------------------------------------------------------------------------- + im(y)| + -------------------------------------------------------------------------------------------------------------- + re(y)|
\  \                                                        2                                                               /                                                         2                                                               / \  \                                                      2                                                               /                                                         2                                                               /
(i(−(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+im⁡(y))−(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+re⁡(y))(i((10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+im⁡(y))+(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+re⁡(y))\left(i \left(- \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{re}{\left(y\right)}\right) \left(i \left(\frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{re}{\left(y\right)}\right) 
=
         2          2                     
     3*re (y)   3*im (y)                  
-8 - -------- + -------- - 3*I*im(y)*re(y)
        2          2
−3(re⁡(y))22−3ire⁡(y)im⁡(y)+3(im⁡(y))22−8- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{2} - 3 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{2} - 8 
-8 - 3*re(y)^2/2 + 3*im(y)^2/2 - 3*i*im(y)*re(y)
Respuesta rápida [src] 
       /      ___________________________________________________                                                               \       ___________________________________________________                                                               
       |     /                             2                         /     /                          2           2   \\        |      /                             2                         /     /                          2           2   \\        
       |  4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |   4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        
       |  \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *sin|-------------------------------------------------|        |   \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *cos|-------------------------------------------------|        
       |                                                             \                        2                        /        |                                                              \                        2                        /        
x1 = I*|- -------------------------------------------------------------------------------------------------------------- + im(y)| - -------------------------------------------------------------------------------------------------------------- + re(y)
       \                                                        2                                                               /                                                         2
x1=i(−(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+im⁡(y))−(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+re⁡(y)x_{1} = i \left(- \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{re}{\left(y\right)} 
       /    ___________________________________________________                                                               \       ___________________________________________________                                                               
       |   /                             2                         /     /                          2           2   \\        |      /                             2                         /     /                          2           2   \\        
       |4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        |   4 /  /          2           2   \          2      2        |atan2\20*im(y)*re(y), 32 - 10*im (y) + 10*re (y)/|        
       |\/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *sin|-------------------------------------------------|        |   \/   \32 - 10*im (y) + 10*re (y)/  + 400*im (y)*re (y) *cos|-------------------------------------------------|        
       |                                                           \                        2                        /        |                                                              \                        2                        /        
x2 = I*|-------------------------------------------------------------------------------------------------------------- + im(y)| + -------------------------------------------------------------------------------------------------------------- + re(y)
       \                                                      2                                                               /                                                         2
x2=i((10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+im⁡(y))+(10(re⁡(y))2−10(im⁡(y))2+32)2+400(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(20re⁡(y)im⁡(y),10(re⁡(y))2−10(im⁡(y))2+32)2)2+re⁡(y)x_{2} = i \left(\frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(20 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},10 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 10 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 32 \right)}}{2} \right)}}{2} + \operatorname{re}{\left(y\right)} 
x2 = i*(((10*re(y)^2 - 10*im(y)^2 + 32)^2 + 400*re(y)^2*im(y)^2)^(1/4)*sin(atan2(20*re(y)*im(y, 10*re(y)^2 - 10*im(y)^2 + 32)/2)/2 + im(y)) + ((10*re(y)^2 - 10*im(y)^2 + 32)^2 + 400*re(y)^2*im(y)^2)^(1/4)*cos(atan2(20*re(y)*im(y), 10*re(y)^2 - 10*im(y)^2 + 32)/2)/2 + re(y))
    © Sr Examen – Калькулятор