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xy²=539(y+1) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   2              
x*y  = 539*(y + 1)
$$x y^{2} = 539 \left(y + 1\right)$$
Solución detallada
Tenemos una ecuación lineal:
x*y^2 = 539*(y+1)

Abrimos los paréntesis en el miembro derecho de la ecuación
x*y^2 = 539*y+539*1

Dividamos ambos miembros de la ecuación en y^2
x = 539 + 539*y / (y^2)

Obtenemos la respuesta: x = 539*(1 + y)/y^2
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$x y^{2} = 539 y + 539$$
Коэффициент при x равен
$$y^{2}$$
entonces son posibles los casos para y :
$$y < 0$$
$$y = 0$$
Consideremos todos los casos con detalles:
Con
$$y < 0$$
la ecuación será
$$x = 0$$
su solución
$$x = 0$$
Con
$$y = 0$$
la ecuación será
$$-539 = 0$$
su solución
no hay soluciones
Gráfica
Respuesta rápida [src]
       //            2                    2       \                                     \               /            2                    2       \          2          
       ||      539*im (y)           539*re (y)    |         1078*(1 + re(y))*im(y)*re(y)|               |      539*im (y)           539*re (y)    |   1078*im (y)*re(y) 
x1 = I*||- ------------------ + ------------------|*im(y) - ----------------------------| + (1 + re(y))*|- ------------------ + ------------------| + ------------------
       ||                   2                    2|                               2     |               |                   2                    2|                    2
       ||  /  2        2   \    /  2        2   \ |              /  2        2   \      |               |  /  2        2   \    /  2        2   \ |   /  2        2   \ 
       \\  \im (y) + re (y)/    \im (y) + re (y)/ /              \im (y) + re (y)/      /               \  \im (y) + re (y)/    \im (y) + re (y)/ /   \im (y) + re (y)/ 
$$x_{1} = i \left(\left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \operatorname{im}{\left(y\right)} - \frac{1078 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\operatorname{re}{\left(y\right)} + 1\right) + \frac{1078 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
x1 = i*((539*re(y)^2/(re(y)^2 + im(y)^2)^2 - 539*im(y)^2/(re(y)^2 + im(y)^2)^2)*im(y) - 1078*(re(y) + 1)*re(y)*im(y)/(re(y)^2 + im(y)^2)^2) + (539*re(y)^2/(re(y)^2 + im(y)^2)^2 - 539*im(y)^2/(re(y)^2 + im(y)^2)^2)*(re(y) + 1) + 1078*re(y)*im(y)^2/(re(y)^2 + im(y)^2)^2
Suma y producto de raíces [src]
suma
  //            2                    2       \                                     \               /            2                    2       \          2          
  ||      539*im (y)           539*re (y)    |         1078*(1 + re(y))*im(y)*re(y)|               |      539*im (y)           539*re (y)    |   1078*im (y)*re(y) 
I*||- ------------------ + ------------------|*im(y) - ----------------------------| + (1 + re(y))*|- ------------------ + ------------------| + ------------------
  ||                   2                    2|                               2     |               |                   2                    2|                    2
  ||  /  2        2   \    /  2        2   \ |              /  2        2   \      |               |  /  2        2   \    /  2        2   \ |   /  2        2   \ 
  \\  \im (y) + re (y)/    \im (y) + re (y)/ /              \im (y) + re (y)/      /               \  \im (y) + re (y)/    \im (y) + re (y)/ /   \im (y) + re (y)/ 
$$i \left(\left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \operatorname{im}{\left(y\right)} - \frac{1078 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\operatorname{re}{\left(y\right)} + 1\right) + \frac{1078 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
=
  //            2                    2       \                                     \               /            2                    2       \          2          
  ||      539*im (y)           539*re (y)    |         1078*(1 + re(y))*im(y)*re(y)|               |      539*im (y)           539*re (y)    |   1078*im (y)*re(y) 
I*||- ------------------ + ------------------|*im(y) - ----------------------------| + (1 + re(y))*|- ------------------ + ------------------| + ------------------
  ||                   2                    2|                               2     |               |                   2                    2|                    2
  ||  /  2        2   \    /  2        2   \ |              /  2        2   \      |               |  /  2        2   \    /  2        2   \ |   /  2        2   \ 
  \\  \im (y) + re (y)/    \im (y) + re (y)/ /              \im (y) + re (y)/      /               \  \im (y) + re (y)/    \im (y) + re (y)/ /   \im (y) + re (y)/ 
$$i \left(\left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \operatorname{im}{\left(y\right)} - \frac{1078 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\operatorname{re}{\left(y\right)} + 1\right) + \frac{1078 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
producto
  //            2                    2       \                                     \               /            2                    2       \          2          
  ||      539*im (y)           539*re (y)    |         1078*(1 + re(y))*im(y)*re(y)|               |      539*im (y)           539*re (y)    |   1078*im (y)*re(y) 
I*||- ------------------ + ------------------|*im(y) - ----------------------------| + (1 + re(y))*|- ------------------ + ------------------| + ------------------
  ||                   2                    2|                               2     |               |                   2                    2|                    2
  ||  /  2        2   \    /  2        2   \ |              /  2        2   \      |               |  /  2        2   \    /  2        2   \ |   /  2        2   \ 
  \\  \im (y) + re (y)/    \im (y) + re (y)/ /              \im (y) + re (y)/      /               \  \im (y) + re (y)/    \im (y) + re (y)/ /   \im (y) + re (y)/ 
$$i \left(\left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \operatorname{im}{\left(y\right)} - \frac{1078 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\operatorname{re}{\left(y\right)} + 1\right) + \frac{1078 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
=
    /            /  2        2   \       2              /  2        2                         \      \
539*\(1 + re(y))*\re (y) - im (y)/ + 2*im (y)*re(y) + I*\re (y) - im (y) - 2*(1 + re(y))*re(y)/*im(y)/
------------------------------------------------------------------------------------------------------
                                                           2                                          
                                          /  2        2   \                                           
                                          \im (y) + re (y)/                                           
$$\frac{539 \left(\left(\operatorname{re}{\left(y\right)} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) + i \left(- 2 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
539*((1 + re(y))*(re(y)^2 - im(y)^2) + 2*im(y)^2*re(y) + i*(re(y)^2 - im(y)^2 - 2*(1 + re(y))*re(y))*im(y))/(im(y)^2 + re(y)^2)^2