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xy=x+y+9 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
x*y = x + y + 9
xy=(x+y)+9x y = \left(x + y\right) + 9
Simplificar
Solución detallada
Tenemos una ecuación lineal:
x*y = x+y+9

Sumamos los términos semejantes en el miembro derecho de la ecuación:
x*y = 9 + x + y

Transportamos los términos con la incógnita x
del miembro derecho al izquierdo:
xy−x=y+9x y - x = y + 9
Dividamos ambos miembros de la ecuación en (-x + x*y)/x
x = 9 + y / ((-x + x*y)/x)

Obtenemos la respuesta: x = (9 + y)/(-1 + y)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
xy=x+y+9x y = x + y + 9
Коэффициент при x равен
y−1y - 1
entonces son posibles los casos para y :
y<1y < 1
y=1y = 1
Consideremos todos los casos con detalles:
Con
y<1y < 1
la ecuación será
−x−9=0- x - 9 = 0
su solución
x=−9x = -9
Con
y=1y = 1
la ecuación será
−10=0-10 = 0
su solución
no hay soluciones
Gráfica
Suma y producto de raíces [src] 
suma
                                                                2                                      
  /  (-1 + re(y))*im(y)       (9 + re(y))*im(y)   \           im (y)           (-1 + re(y))*(9 + re(y))
I*|---------------------- - ----------------------| + ---------------------- + ------------------------
  |            2     2                  2     2   |               2     2                   2     2    
  \(-1 + re(y))  + im (y)   (-1 + re(y))  + im (y)/   (-1 + re(y))  + im (y)    (-1 + re(y))  + im (y)
i((re⁡(y)−1)im⁡(y)(re⁡(y)−1)2+(im⁡(y))2−(re⁡(y)+9)im⁡(y)(re⁡(y)−1)2+(im⁡(y))2)+(re⁡(y)−1)(re⁡(y)+9)(re⁡(y)−1)2+(im⁡(y))2+(im⁡(y))2(re⁡(y)−1)2+(im⁡(y))2i \left(\frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(y\right)} + 9\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \left(\operatorname{re}{\left(y\right)} + 9\right)}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
                                                                2                                      
  /  (-1 + re(y))*im(y)       (9 + re(y))*im(y)   \           im (y)           (-1 + re(y))*(9 + re(y))
I*|---------------------- - ----------------------| + ---------------------- + ------------------------
  |            2     2                  2     2   |               2     2                   2     2    
  \(-1 + re(y))  + im (y)   (-1 + re(y))  + im (y)/   (-1 + re(y))  + im (y)    (-1 + re(y))  + im (y)
i((re⁡(y)−1)im⁡(y)(re⁡(y)−1)2+(im⁡(y))2−(re⁡(y)+9)im⁡(y)(re⁡(y)−1)2+(im⁡(y))2)+(re⁡(y)−1)(re⁡(y)+9)(re⁡(y)−1)2+(im⁡(y))2+(im⁡(y))2(re⁡(y)−1)2+(im⁡(y))2i \left(\frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(y\right)} + 9\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \left(\operatorname{re}{\left(y\right)} + 9\right)}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
producto
                                                                2                                      
  /  (-1 + re(y))*im(y)       (9 + re(y))*im(y)   \           im (y)           (-1 + re(y))*(9 + re(y))
I*|---------------------- - ----------------------| + ---------------------- + ------------------------
  |            2     2                  2     2   |               2     2                   2     2    
  \(-1 + re(y))  + im (y)   (-1 + re(y))  + im (y)/   (-1 + re(y))  + im (y)    (-1 + re(y))  + im (y)
i((re⁡(y)−1)im⁡(y)(re⁡(y)−1)2+(im⁡(y))2−(re⁡(y)+9)im⁡(y)(re⁡(y)−1)2+(im⁡(y))2)+(re⁡(y)−1)(re⁡(y)+9)(re⁡(y)−1)2+(im⁡(y))2+(im⁡(y))2(re⁡(y)−1)2+(im⁡(y))2i \left(\frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(y\right)} + 9\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \left(\operatorname{re}{\left(y\right)} + 9\right)}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
  2                                           
im (y) + (-1 + re(y))*(9 + re(y)) - 10*I*im(y)
----------------------------------------------
                        2     2               
            (-1 + re(y))  + im (y)
(re⁡(y)−1)(re⁡(y)+9)+(im⁡(y))2−10iim⁡(y)(re⁡(y)−1)2+(im⁡(y))2\frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \left(\operatorname{re}{\left(y\right)} + 9\right) + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 10 i \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
(im(y)^2 + (-1 + re(y))*(9 + re(y)) - 10*i*im(y))/((-1 + re(y))^2 + im(y)^2)
Respuesta rápida [src] 
                                                                     2                                      
       /  (-1 + re(y))*im(y)       (9 + re(y))*im(y)   \           im (y)           (-1 + re(y))*(9 + re(y))
x1 = I*|---------------------- - ----------------------| + ---------------------- + ------------------------
       |            2     2                  2     2   |               2     2                   2     2    
       \(-1 + re(y))  + im (y)   (-1 + re(y))  + im (y)/   (-1 + re(y))  + im (y)    (-1 + re(y))  + im (y)
x1=i((re⁡(y)−1)im⁡(y)(re⁡(y)−1)2+(im⁡(y))2−(re⁡(y)+9)im⁡(y)(re⁡(y)−1)2+(im⁡(y))2)+(re⁡(y)−1)(re⁡(y)+9)(re⁡(y)−1)2+(im⁡(y))2+(im⁡(y))2(re⁡(y)−1)2+(im⁡(y))2x_{1} = i \left(\frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(y\right)} + 9\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \left(\operatorname{re}{\left(y\right)} + 9\right)}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
x1 = i*((re(y) - 1)*im(y)/((re(y) - 1)^2 + im(y)^2) - (re(y) + 9)*im(y)/((re(y) - 1)^2 + im(y)^2)) + (re(y) - 1)*(re(y) + 9)/((re(y) - 1)^2 + im(y)^2) + im(y)^2/((re(y) - 1)^2 + im(y)^2)
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