Question 97
Find all real $x, y, z$ so that
$$
\begin{aligned}
& x^2 y + y^2 z + z^2 = 0 \\
& z^3 + z^2 y + z y^3 + x^2 y = \frac{1}{4}(x^4 + y^4)
\end{aligned}
$$
$$
\begin{aligned}
& x^2 y + y^2 z + z^2 = 0 \\
& z^3 + z^2 y + z y^3 + x^2 y = \frac{1}{4}(x^4 + y^4)
\end{aligned}
$$