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Solución de sistemas de ecuaciones/ xy×(x^2+y^2)=10; xy+x^2+y^2=7

xy×(x^2+y^2)=10; xy+x^2+y^2=7

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Solución

Ha introducido [src] 
    / 2    2\     
x*y*\x  + y / = 10
$$x y \left(x^{2} + y^{2}\right) = 10$$ 
       2    2    
x*y + x  + y  = 7
$$y^{2} + \left(x^{2} + x y\right) = 7$$ 
y^2 + x^2 + x*y = 7
Respuesta rápida
$$x_{1} = -2$$
=
$$-2$$
=
-2

$$y_{1} = -1$$
=
$$-1$$
=
-1
$$x_{2} = -1$$
=
$$-1$$
=
-1

$$y_{2} = -2$$
=
$$-2$$
=
-2
$$x_{3} = 1$$
=
$$1$$
=
1

$$y_{3} = 2$$
=
$$2$$
=
2
$$x_{4} = 2$$
=
$$2$$
=
2

$$y_{4} = 1$$
=
$$1$$
=
1
$$x_{5} = \frac{\left(-1 + 2 \sqrt{6} i\right) \sqrt{1 + 2 \sqrt{6} i}}{5}$$
=
$$\frac{\left(-1 + 2 \sqrt{6} i\right) \sqrt{1 + 2 \sqrt{6} i}}{5}$$
=
-1.73205080756888 + 1.4142135623731*i

$$y_{5} = - \sqrt{1 + 2 \sqrt{6} i}$$
=
$$- \sqrt{1 + 2 \sqrt{6} i}$$
=
-1.73205080756888 - 1.4142135623731*i
$$x_{6} = - \frac{\sqrt{1 - 2 \sqrt{6} i} \left(1 + 2 \sqrt{6} i\right)}{5}$$
=
$$- \frac{\sqrt{1 - 2 \sqrt{6} i} \left(1 + 2 \sqrt{6} i\right)}{5}$$
=
-1.73205080756888 - 1.4142135623731*i

$$y_{6} = - \sqrt{1 - 2 \sqrt{6} i}$$
=
$$- \sqrt{1 - 2 \sqrt{6} i}$$
=
-1.73205080756888 + 1.4142135623731*i
$$x_{7} = \frac{\sqrt{1 - 2 \sqrt{6} i} \left(1 + 2 \sqrt{6} i\right)}{5}$$
=
$$\frac{\sqrt{1 - 2 \sqrt{6} i} \left(1 + 2 \sqrt{6} i\right)}{5}$$
=
1.73205080756888 + 1.4142135623731*i

$$y_{7} = \sqrt{1 - 2 \sqrt{6} i}$$
=
$$\sqrt{1 - 2 \sqrt{6} i}$$
=
1.73205080756888 - 1.4142135623731*i
$$x_{8} = \frac{\left(1 - 2 \sqrt{6} i\right) \sqrt{1 + 2 \sqrt{6} i}}{5}$$
=
$$\frac{\left(1 - 2 \sqrt{6} i\right) \sqrt{1 + 2 \sqrt{6} i}}{5}$$
=
1.73205080756888 - 1.4142135623731*i

$$y_{8} = \sqrt{1 + 2 \sqrt{6} i}$$
=
$$\sqrt{1 + 2 \sqrt{6} i}$$
=
1.73205080756888 + 1.4142135623731*i
Respuesta numérica [src] 
x1 = 1.0
y1 = 2.0
x2 = -2.0
y2 = -0.9999999999999999
x3 = 2.0
y3 = 1.0
x4 = -2.0
y4 = -1.0
x5 = 0.9999999999999999
y5 = 2.0
x6 = -1.0
y6 = -2.0
x6 = -1.0
y6 = -2.0
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