Sr Examen

Otras calculadoras

z=2*x^3*y-4*x*y^5 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] 
       3          5
z = 2*x *y - 4*x*y
z=−4xy5+2x3yz = - 4 x y^{5} + 2 x^{3} y
Simplificar
Solución detallada
Tenemos una ecuación lineal:
z = 2*x^3*y-4*x*y^5

Obtenemos la respuesta: z = 2*x*y*(x^2 - 2*y^4)
Gráfica
Respuesta rápida [src] 
       /  /      3                                3         \             /  2        2          4          4           2      2   \        \     /      3                                3         \             /  2        2          4          4           2      2   \        
z1 = I*\2*\- 8*re (y)*im(y) + 2*im(x)*re(x) + 8*im (y)*re(y)/*re(x*y) + 2*\re (x) - im (x) - 2*im (y) - 2*re (y) + 12*im (y)*re (y)/*im(x*y)/ - 2*\- 8*re (y)*im(y) + 2*im(x)*re(x) + 8*im (y)*re(y)/*im(x*y) + 2*\re (x) - im (x) - 2*im (y) - 2*re (y) + 12*im (y)*re (y)/*re(x*y)
z1=i(2(2re⁡(x)im⁡(x)−8(re⁡(y))3im⁡(y)+8re⁡(y)(im⁡(y))3)re⁡(xy)+2((re⁡(x))2−2(re⁡(y))4+12(re⁡(y))2(im⁡(y))2−(im⁡(x))2−2(im⁡(y))4)im⁡(xy))−2(2re⁡(x)im⁡(x)−8(re⁡(y))3im⁡(y)+8re⁡(y)(im⁡(y))3)im⁡(xy)+2((re⁡(x))2−2(re⁡(y))4+12(re⁡(y))2(im⁡(y))2−(im⁡(x))2−2(im⁡(y))4)re⁡(xy)z_{1} = i \left(2 \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{re}{\left(x y\right)} + 2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} + 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{im}{\left(x y\right)}\right) - 2 \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{im}{\left(x y\right)} + 2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} + 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{re}{\left(x y\right)} 
z1 = i*(2*(2*re(x)*im(x) - 8*re(y)^3*im(y) + 8*re(y)*im(y)^3)*re(x*y) + 2*(re(x)^2 - 2*re(y)^4 + 12*re(y)^2*im(y)^2 - im(x)^2 - 2*im(y)^4)*im(x*y)) - 2*(2*re(x)*im(x) - 8*re(y)^3*im(y) + 8*re(y)*im(y)^3)*im(x*y) + 2*(re(x)^2 - 2*re(y)^4 + 12*re(y)^2*im(y)^2 - im(x)^2 - 2*im(y)^4)*re(x*y)
Suma y producto de raíces [src] 
suma
  /  /      3                                3         \             /  2        2          4          4           2      2   \        \     /      3                                3         \             /  2        2          4          4           2      2   \        
I*\2*\- 8*re (y)*im(y) + 2*im(x)*re(x) + 8*im (y)*re(y)/*re(x*y) + 2*\re (x) - im (x) - 2*im (y) - 2*re (y) + 12*im (y)*re (y)/*im(x*y)/ - 2*\- 8*re (y)*im(y) + 2*im(x)*re(x) + 8*im (y)*re(y)/*im(x*y) + 2*\re (x) - im (x) - 2*im (y) - 2*re (y) + 12*im (y)*re (y)/*re(x*y)
i(2(2re⁡(x)im⁡(x)−8(re⁡(y))3im⁡(y)+8re⁡(y)(im⁡(y))3)re⁡(xy)+2((re⁡(x))2−2(re⁡(y))4+12(re⁡(y))2(im⁡(y))2−(im⁡(x))2−2(im⁡(y))4)im⁡(xy))−2(2re⁡(x)im⁡(x)−8(re⁡(y))3im⁡(y)+8re⁡(y)(im⁡(y))3)im⁡(xy)+2((re⁡(x))2−2(re⁡(y))4+12(re⁡(y))2(im⁡(y))2−(im⁡(x))2−2(im⁡(y))4)re⁡(xy)i \left(2 \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{re}{\left(x y\right)} + 2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} + 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{im}{\left(x y\right)}\right) - 2 \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{im}{\left(x y\right)} + 2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} + 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{re}{\left(x y\right)} 
=
  /  /      3                                3         \             /  2        2          4          4           2      2   \        \     /      3                                3         \             /  2        2          4          4           2      2   \        
I*\2*\- 8*re (y)*im(y) + 2*im(x)*re(x) + 8*im (y)*re(y)/*re(x*y) + 2*\re (x) - im (x) - 2*im (y) - 2*re (y) + 12*im (y)*re (y)/*im(x*y)/ - 2*\- 8*re (y)*im(y) + 2*im(x)*re(x) + 8*im (y)*re(y)/*im(x*y) + 2*\re (x) - im (x) - 2*im (y) - 2*re (y) + 12*im (y)*re (y)/*re(x*y)
i(2(2re⁡(x)im⁡(x)−8(re⁡(y))3im⁡(y)+8re⁡(y)(im⁡(y))3)re⁡(xy)+2((re⁡(x))2−2(re⁡(y))4+12(re⁡(y))2(im⁡(y))2−(im⁡(x))2−2(im⁡(y))4)im⁡(xy))−2(2re⁡(x)im⁡(x)−8(re⁡(y))3im⁡(y)+8re⁡(y)(im⁡(y))3)im⁡(xy)+2((re⁡(x))2−2(re⁡(y))4+12(re⁡(y))2(im⁡(y))2−(im⁡(x))2−2(im⁡(y))4)re⁡(xy)i \left(2 \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{re}{\left(x y\right)} + 2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} + 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{im}{\left(x y\right)}\right) - 2 \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{im}{\left(x y\right)} + 2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} + 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{re}{\left(x y\right)} 
producto
  /  /      3                                3         \             /  2        2          4          4           2      2   \        \     /      3                                3         \             /  2        2          4          4           2      2   \        
I*\2*\- 8*re (y)*im(y) + 2*im(x)*re(x) + 8*im (y)*re(y)/*re(x*y) + 2*\re (x) - im (x) - 2*im (y) - 2*re (y) + 12*im (y)*re (y)/*im(x*y)/ - 2*\- 8*re (y)*im(y) + 2*im(x)*re(x) + 8*im (y)*re(y)/*im(x*y) + 2*\re (x) - im (x) - 2*im (y) - 2*re (y) + 12*im (y)*re (y)/*re(x*y)
i(2(2re⁡(x)im⁡(x)−8(re⁡(y))3im⁡(y)+8re⁡(y)(im⁡(y))3)re⁡(xy)+2((re⁡(x))2−2(re⁡(y))4+12(re⁡(y))2(im⁡(y))2−(im⁡(x))2−2(im⁡(y))4)im⁡(xy))−2(2re⁡(x)im⁡(x)−8(re⁡(y))3im⁡(y)+8re⁡(y)(im⁡(y))3)im⁡(xy)+2((re⁡(x))2−2(re⁡(y))4+12(re⁡(y))2(im⁡(y))2−(im⁡(x))2−2(im⁡(y))4)re⁡(xy)i \left(2 \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{re}{\left(x y\right)} + 2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} + 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{im}{\left(x y\right)}\right) - 2 \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{im}{\left(x y\right)} + 2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} + 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{re}{\left(x y\right)} 
=
    /                  3                3         \             /  2        2          4          4           2      2   \               /  /  2        2          4          4           2      2   \             /                  3                3         \        \
- 4*\im(x)*re(x) - 4*re (y)*im(y) + 4*im (y)*re(y)/*im(x*y) - 2*\im (x) - re (x) + 2*im (y) + 2*re (y) - 12*im (y)*re (y)/*re(x*y) + 2*I*\- \im (x) - re (x) + 2*im (y) + 2*re (y) - 12*im (y)*re (y)/*im(x*y) + 2*\im(x)*re(x) - 4*re (y)*im(y) + 4*im (y)*re(y)/*re(x*y)/
2i(2(re⁡(x)im⁡(x)−4(re⁡(y))3im⁡(y)+4re⁡(y)(im⁡(y))3)re⁡(xy)−(−(re⁡(x))2+2(re⁡(y))4−12(re⁡(y))2(im⁡(y))2+(im⁡(x))2+2(im⁡(y))4)im⁡(xy))−4(re⁡(x)im⁡(x)−4(re⁡(y))3im⁡(y)+4re⁡(y)(im⁡(y))3)im⁡(xy)−2(−(re⁡(x))2+2(re⁡(y))4−12(re⁡(y))2(im⁡(y))2+(im⁡(x))2+2(im⁡(y))4)re⁡(xy)2 i \left(2 \left(\operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 4 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{re}{\left(x y\right)} - \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{im}{\left(x y\right)}\right) - 4 \left(\operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} + 4 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3}\right) \operatorname{im}{\left(x y\right)} - 2 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right) \operatorname{re}{\left(x y\right)} 
-4*(im(x)*re(x) - 4*re(y)^3*im(y) + 4*im(y)^3*re(y))*im(x*y) - 2*(im(x)^2 - re(x)^2 + 2*im(y)^4 + 2*re(y)^4 - 12*im(y)^2*re(y)^2)*re(x*y) + 2*i*(-(im(x)^2 - re(x)^2 + 2*im(y)^4 + 2*re(y)^4 - 12*im(y)^2*re(y)^2)*im(x*y) + 2*(im(x)*re(x) - 4*re(y)^3*im(y) + 4*im(y)^3*re(y))*re(x*y))
    © Sr Examen – Калькулятор