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x+y=3*x2-x*y-y2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
x + y = 3*x2 - x*y - y2
x+y=−y2+(−xy+3x2)x + y = - y_{2} + \left(- x y + 3 x_{2}\right)
Simplificar
Solución detallada
Tenemos una ecuación lineal:
x+y = 3*x2-x*y-y2

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
x + y = 3*x2-x*y-y2

Sumamos los términos semejantes en el miembro derecho de la ecuación:
x + y = -y2 + 3*x2 - x*y

Move the summands with the other variables
del miembro izquierdo al derecho, obtenemos:
x=−xy+3x2−y−y2x = - x y + 3 x_{2} - y - y_{2}
Obtenemos la respuesta: x = (-y - y2 + 3*x2)/(1 + y)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
x+y=−xy+3x2−y2x + y = - x y + 3 x_{2} - y_{2}
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−3x2+y2−2=0- x - 3 x_{2} + y_{2} - 2 = 0
su solución
x=−3x2+y2−2x = - 3 x_{2} + y_{2} - 2
Con
y=−1y = -1
la ecuación será
−3x2+y2−1=0- 3 x_{2} + y_{2} - 1 = 0
su solución
Gráfica
Suma y producto de raíces [src] 
suma
  /(1 + re(y))*(-im(y) - im(y2) + 3*im(x2))   (-re(y) - re(y2) + 3*re(x2))*im(y)\   (1 + re(y))*(-re(y) - re(y2) + 3*re(x2))   (-im(y) - im(y2) + 3*im(x2))*im(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)(3im⁡(x2)−im⁡(y)−im⁡(y2))(re⁡(y)+1)2+(im⁡(y))2−(3re⁡(x2)−re⁡(y)−re⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2)+(re⁡(y)+1)(3re⁡(x2)−re⁡(y)−re⁡(y2))(re⁡(y)+1)2+(im⁡(y))2+(3im⁡(x2)−im⁡(y)−im⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2i \left(\frac{\left(\operatorname{re}{\left(y\right)} + 1\right) \left(3 \operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y_{2}\right)}\right)}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(3 \operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(y_{2}\right)}\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(3 \operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(y_{2}\right)}\right)}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(3 \operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y_{2}\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
  /(1 + re(y))*(-im(y) - im(y2) + 3*im(x2))   (-re(y) - re(y2) + 3*re(x2))*im(y)\   (1 + re(y))*(-re(y) - re(y2) + 3*re(x2))   (-im(y) - im(y2) + 3*im(x2))*im(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)(3im⁡(x2)−im⁡(y)−im⁡(y2))(re⁡(y)+1)2+(im⁡(y))2−(3re⁡(x2)−re⁡(y)−re⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2)+(re⁡(y)+1)(3re⁡(x2)−re⁡(y)−re⁡(y2))(re⁡(y)+1)2+(im⁡(y))2+(3im⁡(x2)−im⁡(y)−im⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2i \left(\frac{\left(\operatorname{re}{\left(y\right)} + 1\right) \left(3 \operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y_{2}\right)}\right)}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(3 \operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(y_{2}\right)}\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(3 \operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(y_{2}\right)}\right)}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(3 \operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y_{2}\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
producto
  /(1 + re(y))*(-im(y) - im(y2) + 3*im(x2))   (-re(y) - re(y2) + 3*re(x2))*im(y)\   (1 + re(y))*(-re(y) - re(y2) + 3*re(x2))   (-im(y) - im(y2) + 3*im(x2))*im(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)(3im⁡(x2)−im⁡(y)−im⁡(y2))(re⁡(y)+1)2+(im⁡(y))2−(3re⁡(x2)−re⁡(y)−re⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2)+(re⁡(y)+1)(3re⁡(x2)−re⁡(y)−re⁡(y2))(re⁡(y)+1)2+(im⁡(y))2+(3im⁡(x2)−im⁡(y)−im⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2i \left(\frac{\left(\operatorname{re}{\left(y\right)} + 1\right) \left(3 \operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y_{2}\right)}\right)}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(3 \operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(y_{2}\right)}\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(3 \operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(y_{2}\right)}\right)}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(3 \operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y_{2}\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
I*((-3*re(x2) + re(y) + re(y2))*im(y) - (1 + re(y))*(-3*im(x2) + im(y) + im(y2))) - (1 + re(y))*(-3*re(x2) + re(y) + re(y2)) - (-3*im(x2) + im(y) + im(y2))*im(y)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 2     2                                                                         
                                                                      (1 + re(y))  + im (y)
i(−(re⁡(y)+1)(−3im⁡(x2)+im⁡(y)+im⁡(y2))+(−3re⁡(x2)+re⁡(y)+re⁡(y2))im⁡(y))−(re⁡(y)+1)(−3re⁡(x2)+re⁡(y)+re⁡(y2))−(−3im⁡(x2)+im⁡(y)+im⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2\frac{i \left(- \left(\operatorname{re}{\left(y\right)} + 1\right) \left(- 3 \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y_{2}\right)}\right) + \left(- 3 \operatorname{re}{\left(x_{2}\right)} + \operatorname{re}{\left(y\right)} + \operatorname{re}{\left(y_{2}\right)}\right) \operatorname{im}{\left(y\right)}\right) - \left(\operatorname{re}{\left(y\right)} + 1\right) \left(- 3 \operatorname{re}{\left(x_{2}\right)} + \operatorname{re}{\left(y\right)} + \operatorname{re}{\left(y_{2}\right)}\right) - \left(- 3 \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y_{2}\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
(i*((-3*re(x2) + re(y) + re(y2))*im(y) - (1 + re(y))*(-3*im(x2) + im(y) + im(y2))) - (1 + re(y))*(-3*re(x2) + re(y) + re(y2)) - (-3*im(x2) + im(y) + im(y2))*im(y))/((1 + re(y))^2 + im(y)^2)
Respuesta rápida [src] 
       /(1 + re(y))*(-im(y) - im(y2) + 3*im(x2))   (-re(y) - re(y2) + 3*re(x2))*im(y)\   (1 + re(y))*(-re(y) - re(y2) + 3*re(x2))   (-im(y) - im(y2) + 3*im(x2))*im(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)(3im⁡(x2)−im⁡(y)−im⁡(y2))(re⁡(y)+1)2+(im⁡(y))2−(3re⁡(x2)−re⁡(y)−re⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2)+(re⁡(y)+1)(3re⁡(x2)−re⁡(y)−re⁡(y2))(re⁡(y)+1)2+(im⁡(y))2+(3im⁡(x2)−im⁡(y)−im⁡(y2))im⁡(y)(re⁡(y)+1)2+(im⁡(y))2x_{1} = i \left(\frac{\left(\operatorname{re}{\left(y\right)} + 1\right) \left(3 \operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y_{2}\right)}\right)}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(3 \operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(y_{2}\right)}\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(3 \operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(y_{2}\right)}\right)}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(3 \operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y_{2}\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
x1 = i*((re(y) + 1)*(3*im(x2) - im(y) - im(y2))/((re(y) + 1)^2 + im(y)^2) - (3*re(x2) - re(y) - re(y2))*im(y)/((re(y) + 1)^2 + im(y)^2)) + (re(y) + 1)*(3*re(x2) - re(y) - re(y2))/((re(y) + 1)^2 + im(y)^2) + (3*im(x2) - im(y) - im(y2))*im(y)/((re(y) + 1)^2 + im(y)^2)
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