Question 76
Find the number of real solutions of the system
$$
\left\lvert\,
\begin{aligned}
& x + y + z = 3 x y \\
& x^{2} + y^{2} + z^{2} = 3 x z \\
& x^{3} + y^{3} + z^{3} = 3 y z
\end{aligned}
\right.
$$
$$
\left\lvert\,
\begin{aligned}
& x + y + z = 3 x y \\
& x^{2} + y^{2} + z^{2} = 3 x z \\
& x^{3} + y^{3} + z^{3} = 3 y z
\end{aligned}
\right.
$$