Question 165
Find all $x$, $y$, $z$ which satisfy:
$$
\begin{cases} x^2 + x y + x z = y, \\ y^2 + y z + y x = z, \\ z^2 + z x + z y = x. \end{cases}
$$
$$
\begin{cases} x^2 + x y + x z = y, \\ y^2 + y z + y x = z, \\ z^2 + z x + z y = x. \end{cases}
$$