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Solución de sistemas de ecuaciones/ xy+a+by+bx=0; yz+a+bz+by=0; xz+a+bx+bz=0; x+y+z=5; xy+xz+yz=1

xy+a+by+bx=0; yz+a+bz+by=0; xz+a+bx+bz=0; x+y+z=5; xy+xz+yz=1

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Gráfico:

interior superior

interior superior

Solución

Ha introducido [src] 
x*y + a + b*y + b*x = 0
bx+(by+(a+xy))=0b x + \left(b y + \left(a + x y\right)\right) = 0 
y*z + a + b*z + b*y = 0
by+(bz+(a+yz))=0b y + \left(b z + \left(a + y z\right)\right) = 0 
x*z + a + b*x + b*z = 0
bz+(bx+(a+xz))=0b z + \left(b x + \left(a + x z\right)\right) = 0 
x + y + z = 5
z+(x+y)=5z + \left(x + y\right) = 5 
x*y + x*z + y*z = 1
yz+(xy+xz)=1y z + \left(x y + x z\right) = 1 
y*z + x*y + x*z = 1
Respuesta rápida
a1=479−10229a_{1} = \frac{47}{9} - \frac{10 \sqrt{22}}{9}
=
479−10229\frac{47}{9} - \frac{10 \sqrt{22}}{9}
=
0.0106491557517449

b1=−53+223b_{1} = - \frac{5}{3} + \frac{\sqrt{22}}{3}
=
−53+223- \frac{5}{3} + \frac{\sqrt{22}}{3}
=
-0.103194746725523

x1=53−223x_{1} = \frac{5}{3} - \frac{\sqrt{22}}{3}
=
53−223\frac{5}{3} - \frac{\sqrt{22}}{3}
=
0.103194746725523

y1=53−223y_{1} = \frac{5}{3} - \frac{\sqrt{22}}{3}
=
53−223\frac{5}{3} - \frac{\sqrt{22}}{3}
=
0.103194746725523

z1=53+2223z_{1} = \frac{5}{3} + \frac{2 \sqrt{22}}{3}
=
53+2223\frac{5}{3} + \frac{2 \sqrt{22}}{3}
=
4.79361050654895
a2=479−10229a_{2} = \frac{47}{9} - \frac{10 \sqrt{22}}{9}
=
479−10229\frac{47}{9} - \frac{10 \sqrt{22}}{9}
=
0.0106491557517449

b2=−53+223b_{2} = - \frac{5}{3} + \frac{\sqrt{22}}{3}
=
−53+223- \frac{5}{3} + \frac{\sqrt{22}}{3}
=
-0.103194746725523

x2=53−223x_{2} = \frac{5}{3} - \frac{\sqrt{22}}{3}
=
53−223\frac{5}{3} - \frac{\sqrt{22}}{3}
=
0.103194746725523

y2=53+2223y_{2} = \frac{5}{3} + \frac{2 \sqrt{22}}{3}
=
53+2223\frac{5}{3} + \frac{2 \sqrt{22}}{3}
=
4.79361050654895

z2=53−223z_{2} = \frac{5}{3} - \frac{\sqrt{22}}{3}
=
53−223\frac{5}{3} - \frac{\sqrt{22}}{3}
=
0.103194746725523
a3=479−10229a_{3} = \frac{47}{9} - \frac{10 \sqrt{22}}{9}
=
479−10229\frac{47}{9} - \frac{10 \sqrt{22}}{9}
=
0.0106491557517449

b3=−53+223b_{3} = - \frac{5}{3} + \frac{\sqrt{22}}{3}
=
−53+223- \frac{5}{3} + \frac{\sqrt{22}}{3}
=
-0.103194746725523

x3=53+2223x_{3} = \frac{5}{3} + \frac{2 \sqrt{22}}{3}
=
53+2223\frac{5}{3} + \frac{2 \sqrt{22}}{3}
=
4.79361050654895

y3=53−223y_{3} = \frac{5}{3} - \frac{\sqrt{22}}{3}
=
53−223\frac{5}{3} - \frac{\sqrt{22}}{3}
=
0.103194746725523

z3=53−223z_{3} = \frac{5}{3} - \frac{\sqrt{22}}{3}
=
53−223\frac{5}{3} - \frac{\sqrt{22}}{3}
=
0.103194746725523
a4=10229+479a_{4} = \frac{10 \sqrt{22}}{9} + \frac{47}{9}
=
10229+479\frac{10 \sqrt{22}}{9} + \frac{47}{9}
=
10.4337952886927

b4=−53−223b_{4} = - \frac{5}{3} - \frac{\sqrt{22}}{3}
=
−53−223- \frac{5}{3} - \frac{\sqrt{22}}{3}
=
-3.23013858660781

x4=53−2223x_{4} = \frac{5}{3} - \frac{2 \sqrt{22}}{3}
=
53−2223\frac{5}{3} - \frac{2 \sqrt{22}}{3}
=
-1.46027717321562

y4=223+53y_{4} = \frac{\sqrt{22}}{3} + \frac{5}{3}
=
223+53\frac{\sqrt{22}}{3} + \frac{5}{3}
=
3.23013858660781

z4=223+53z_{4} = \frac{\sqrt{22}}{3} + \frac{5}{3}
=
223+53\frac{\sqrt{22}}{3} + \frac{5}{3}
=
3.23013858660781
a5=10229+479a_{5} = \frac{10 \sqrt{22}}{9} + \frac{47}{9}
=
10229+479\frac{10 \sqrt{22}}{9} + \frac{47}{9}
=
10.4337952886927

b5=−53−223b_{5} = - \frac{5}{3} - \frac{\sqrt{22}}{3}
=
−53−223- \frac{5}{3} - \frac{\sqrt{22}}{3}
=
-3.23013858660781

x5=223+53x_{5} = \frac{\sqrt{22}}{3} + \frac{5}{3}
=
223+53\frac{\sqrt{22}}{3} + \frac{5}{3}
=
3.23013858660781

y5=53−2223y_{5} = \frac{5}{3} - \frac{2 \sqrt{22}}{3}
=
53−2223\frac{5}{3} - \frac{2 \sqrt{22}}{3}
=
-1.46027717321562

z5=223+53z_{5} = \frac{\sqrt{22}}{3} + \frac{5}{3}
=
223+53\frac{\sqrt{22}}{3} + \frac{5}{3}
=
3.23013858660781
a6=10229+479a_{6} = \frac{10 \sqrt{22}}{9} + \frac{47}{9}
=
10229+479\frac{10 \sqrt{22}}{9} + \frac{47}{9}
=
10.4337952886927

b6=−53−223b_{6} = - \frac{5}{3} - \frac{\sqrt{22}}{3}
=
−53−223- \frac{5}{3} - \frac{\sqrt{22}}{3}
=
-3.23013858660781

x6=223+53x_{6} = \frac{\sqrt{22}}{3} + \frac{5}{3}
=
223+53\frac{\sqrt{22}}{3} + \frac{5}{3}
=
3.23013858660781

y6=223+53y_{6} = \frac{\sqrt{22}}{3} + \frac{5}{3}
=
223+53\frac{\sqrt{22}}{3} + \frac{5}{3}
=
3.23013858660781

z6=53−2223z_{6} = \frac{5}{3} - \frac{2 \sqrt{22}}{3}
=
53−2223\frac{5}{3} - \frac{2 \sqrt{22}}{3}
=
-1.46027717321562
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