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yz+2x*a+b=0; xz+2y*a+b=0; xy+2z*a+b=0; x^2+y^2+z^2-1=0; x+y+z=0

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Solución

Ha introducido [src]
y*z + 2*x*a + b = 0
$$b + \left(a 2 x + y z\right) = 0$$
x*z + 2*y*a + b = 0
$$b + \left(a 2 y + x z\right) = 0$$
x*y + 2*z*a + b = 0
$$b + \left(a 2 z + x y\right) = 0$$
 2    2    2        
x  + y  + z  - 1 = 0
$$\left(z^{2} + \left(x^{2} + y^{2}\right)\right) - 1 = 0$$
x + y + z = 0
$$z + \left(x + y\right) = 0$$
z + x + y = 0
Respuesta rápida
$$a_{1} = - \frac{\sqrt{6}}{12}$$
=
$$- \frac{\sqrt{6}}{12}$$
=
-0.204124145231932

$$b_{1} = \frac{1}{6}$$
=
$$\frac{1}{6}$$
=
0.166666666666667

$$x_{1} = - \frac{\sqrt{6}}{6}$$
=
$$- \frac{\sqrt{6}}{6}$$
=
-0.408248290463863

$$y_{1} = - \frac{\sqrt{6}}{6}$$
=
$$- \frac{\sqrt{6}}{6}$$
=
-0.408248290463863

$$z_{1} = \frac{\sqrt{6}}{3}$$
=
$$\frac{\sqrt{6}}{3}$$
=
0.816496580927726
$$a_{2} = - \frac{\sqrt{6}}{12}$$
=
$$- \frac{\sqrt{6}}{12}$$
=
-0.204124145231932

$$b_{2} = \frac{1}{6}$$
=
$$\frac{1}{6}$$
=
0.166666666666667

$$x_{2} = - \frac{\sqrt{6}}{6}$$
=
$$- \frac{\sqrt{6}}{6}$$
=
-0.408248290463863

$$y_{2} = \frac{\sqrt{6}}{3}$$
=
$$\frac{\sqrt{6}}{3}$$
=
0.816496580927726

$$z_{2} = - \frac{\sqrt{6}}{6}$$
=
$$- \frac{\sqrt{6}}{6}$$
=
-0.408248290463863
$$a_{3} = - \frac{\sqrt{6}}{12}$$
=
$$- \frac{\sqrt{6}}{12}$$
=
-0.204124145231932

$$b_{3} = \frac{1}{6}$$
=
$$\frac{1}{6}$$
=
0.166666666666667

$$x_{3} = \frac{\sqrt{6}}{3}$$
=
$$\frac{\sqrt{6}}{3}$$
=
0.816496580927726

$$y_{3} = - \frac{\sqrt{6}}{6}$$
=
$$- \frac{\sqrt{6}}{6}$$
=
-0.408248290463863

$$z_{3} = - \frac{\sqrt{6}}{6}$$
=
$$- \frac{\sqrt{6}}{6}$$
=
-0.408248290463863
$$a_{4} = \frac{\sqrt{6}}{12}$$
=
$$\frac{\sqrt{6}}{12}$$
=
0.204124145231932

$$b_{4} = \frac{1}{6}$$
=
$$\frac{1}{6}$$
=
0.166666666666667

$$x_{4} = - \frac{\sqrt{6}}{3}$$
=
$$- \frac{\sqrt{6}}{3}$$
=
-0.816496580927726

$$y_{4} = \frac{\sqrt{6}}{6}$$
=
$$\frac{\sqrt{6}}{6}$$
=
0.408248290463863

$$z_{4} = \frac{\sqrt{6}}{6}$$
=
$$\frac{\sqrt{6}}{6}$$
=
0.408248290463863
$$a_{5} = \frac{\sqrt{6}}{12}$$
=
$$\frac{\sqrt{6}}{12}$$
=
0.204124145231932

$$b_{5} = \frac{1}{6}$$
=
$$\frac{1}{6}$$
=
0.166666666666667

$$x_{5} = \frac{\sqrt{6}}{6}$$
=
$$\frac{\sqrt{6}}{6}$$
=
0.408248290463863

$$y_{5} = - \frac{\sqrt{6}}{3}$$
=
$$- \frac{\sqrt{6}}{3}$$
=
-0.816496580927726

$$z_{5} = \frac{\sqrt{6}}{6}$$
=
$$\frac{\sqrt{6}}{6}$$
=
0.408248290463863
$$a_{6} = \frac{\sqrt{6}}{12}$$
=
$$\frac{\sqrt{6}}{12}$$
=
0.204124145231932

$$b_{6} = \frac{1}{6}$$
=
$$\frac{1}{6}$$
=
0.166666666666667

$$x_{6} = \frac{\sqrt{6}}{6}$$
=
$$\frac{\sqrt{6}}{6}$$
=
0.408248290463863

$$y_{6} = \frac{\sqrt{6}}{6}$$
=
$$\frac{\sqrt{6}}{6}$$
=
0.408248290463863

$$z_{6} = - \frac{\sqrt{6}}{3}$$
=
$$- \frac{\sqrt{6}}{3}$$
=
-0.816496580927726