Question 78
Find all triples $x, y, z$ of real numbers such that the following system holds:
$$
\begin{cases} x^3 + y = z^2 \\ y^3 + z = x^2 \\ z^3 + x = y^2 \end{cases}
$$
$$
\begin{cases} x^3 + y = z^2 \\ y^3 + z = x^2 \\ z^3 + x = y^2 \end{cases}
$$