20. Solve the system of equations:

$$
\left\{\begin{array}{l}
(x+y)^{3}=z \\
(y+z)^{3}=x \\
(z+x)^{3}=y
\end{array}\right.
$$
85.20. Answer. $x=y=z=0 ; \quad x=y=z=1 / \sqrt{8} ; \quad x=y=$ $=z=-1 / \sqrt{8}$.