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xyz=78; x+y+z=0

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Solución

Ha introducido [src]
x*y*z = 78
$$z x y = 78$$
x + y + z = 0
$$z + \left(x + y\right) = 0$$
z + x + y = 0
Respuesta rápida
$$x_{1} = - \frac{z}{2} - \frac{\sqrt{z \left(z^{3} - 312\right)}}{2 z}$$
=
$$- \frac{z^{2} + \sqrt{z \left(z^{3} - 312\right)}}{2 z}$$
=
-0.5*z - 0.5*(z*(-312 + z^3))^0.5/z

$$y_{1} = - \frac{z}{2} + \frac{\sqrt{z \left(z^{3} - 312\right)}}{2 z}$$
=
$$\frac{- z^{2} + \sqrt{z \left(z^{3} - 312\right)}}{2 z}$$
=
-0.5*z + 0.5*(z*(-312 + z^3))^0.5/z
$$x_{2} = - \frac{z}{2} + \frac{\sqrt{z \left(z^{3} - 312\right)}}{2 z}$$
=
$$\frac{- z^{2} + \sqrt{z \left(z^{3} - 312\right)}}{2 z}$$
=
-0.5*z + 0.5*(z*(-312 + z^3))^0.5/z

$$y_{2} = - \frac{z}{2} - \frac{\sqrt{z \left(z^{3} - 312\right)}}{2 z}$$
=
$$- \frac{z^{2} + \sqrt{z \left(z^{3} - 312\right)}}{2 z}$$
=
-0.5*z - 0.5*(z*(-312 + z^3))^0.5/z