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Solución de sistemas de ecuaciones/ yz+2x*k+s=0; xz+2y*k+s=0; xy+2z*k+s=0; x^2+y^2+z^2-1=0; x+y+z=0

yz+2x*k+s=0; xz+2y*k+s=0; xy+2z*k+s=0; x^2+y^2+z^2-1=0; x+y+z=0

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Gráfico:

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interior superior

Solución

Ha introducido [src] 
y*z + 2*x*k + s = 0
s+(k2x+yz)=0s + \left(k 2 x + y z\right) = 0 
x*z + 2*y*k + s = 0
s+(k2y+xz)=0s + \left(k 2 y + x z\right) = 0 
x*y + 2*z*k + s = 0
s+(k2z+xy)=0s + \left(k 2 z + x y\right) = 0 
 2    2    2        
x  + y  + z  - 1 = 0
(z2+(x2+y2))−1=0\left(z^{2} + \left(x^{2} + y^{2}\right)\right) - 1 = 0 
x + y + z = 0
z+(x+y)=0z + \left(x + y\right) = 0 
z + x + y = 0
Respuesta rápida
k1=−612k_{1} = - \frac{\sqrt{6}}{12}
=
−612- \frac{\sqrt{6}}{12}
=
-0.204124145231932

s1=16s_{1} = \frac{1}{6}
=
16\frac{1}{6}
=
0.166666666666667

x1=−66x_{1} = - \frac{\sqrt{6}}{6}
=
−66- \frac{\sqrt{6}}{6}
=
-0.408248290463863

y1=−66y_{1} = - \frac{\sqrt{6}}{6}
=
−66- \frac{\sqrt{6}}{6}
=
-0.408248290463863

z1=63z_{1} = \frac{\sqrt{6}}{3}
=
63\frac{\sqrt{6}}{3}
=
0.816496580927726
k2=−612k_{2} = - \frac{\sqrt{6}}{12}
=
−612- \frac{\sqrt{6}}{12}
=
-0.204124145231932

s2=16s_{2} = \frac{1}{6}
=
16\frac{1}{6}
=
0.166666666666667

x2=−66x_{2} = - \frac{\sqrt{6}}{6}
=
−66- \frac{\sqrt{6}}{6}
=
-0.408248290463863

y2=63y_{2} = \frac{\sqrt{6}}{3}
=
63\frac{\sqrt{6}}{3}
=
0.816496580927726

z2=−66z_{2} = - \frac{\sqrt{6}}{6}
=
−66- \frac{\sqrt{6}}{6}
=
-0.408248290463863
k3=−612k_{3} = - \frac{\sqrt{6}}{12}
=
−612- \frac{\sqrt{6}}{12}
=
-0.204124145231932

s3=16s_{3} = \frac{1}{6}
=
16\frac{1}{6}
=
0.166666666666667

x3=63x_{3} = \frac{\sqrt{6}}{3}
=
63\frac{\sqrt{6}}{3}
=
0.816496580927726

y3=−66y_{3} = - \frac{\sqrt{6}}{6}
=
−66- \frac{\sqrt{6}}{6}
=
-0.408248290463863

z3=−66z_{3} = - \frac{\sqrt{6}}{6}
=
−66- \frac{\sqrt{6}}{6}
=
-0.408248290463863
k4=612k_{4} = \frac{\sqrt{6}}{12}
=
612\frac{\sqrt{6}}{12}
=
0.204124145231932

s4=16s_{4} = \frac{1}{6}
=
16\frac{1}{6}
=
0.166666666666667

x4=−63x_{4} = - \frac{\sqrt{6}}{3}
=
−63- \frac{\sqrt{6}}{3}
=
-0.816496580927726

y4=66y_{4} = \frac{\sqrt{6}}{6}
=
66\frac{\sqrt{6}}{6}
=
0.408248290463863

z4=66z_{4} = \frac{\sqrt{6}}{6}
=
66\frac{\sqrt{6}}{6}
=
0.408248290463863
k5=612k_{5} = \frac{\sqrt{6}}{12}
=
612\frac{\sqrt{6}}{12}
=
0.204124145231932

s5=16s_{5} = \frac{1}{6}
=
16\frac{1}{6}
=
0.166666666666667

x5=66x_{5} = \frac{\sqrt{6}}{6}
=
66\frac{\sqrt{6}}{6}
=
0.408248290463863

y5=−63y_{5} = - \frac{\sqrt{6}}{3}
=
−63- \frac{\sqrt{6}}{3}
=
-0.816496580927726

z5=66z_{5} = \frac{\sqrt{6}}{6}
=
66\frac{\sqrt{6}}{6}
=
0.408248290463863
k6=612k_{6} = \frac{\sqrt{6}}{12}
=
612\frac{\sqrt{6}}{12}
=
0.204124145231932

s6=16s_{6} = \frac{1}{6}
=
16\frac{1}{6}
=
0.166666666666667

x6=66x_{6} = \frac{\sqrt{6}}{6}
=
66\frac{\sqrt{6}}{6}
=
0.408248290463863

y6=66y_{6} = \frac{\sqrt{6}}{6}
=
66\frac{\sqrt{6}}{6}
=
0.408248290463863

z6=−63z_{6} = - \frac{\sqrt{6}}{3}
=
−63- \frac{\sqrt{6}}{3}
=
-0.816496580927726
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