Question 97
Find all ordered triples $(x, y, z)$ of real numbers satisfying the following system of equations:
$$
\begin{aligned}
x^{3} & = \frac{z}{y} - 2 \frac{y}{z} \\
y^{3} & = \frac{x}{z} - 2 \frac{z}{x} \\
z^{3} & = \frac{y}{x} - 2 \frac{x}{y}
\end{aligned}
$$
$$
\begin{aligned}
x^{3} & = \frac{z}{y} - 2 \frac{y}{z} \\
y^{3} & = \frac{x}{z} - 2 \frac{z}{x} \\
z^{3} & = \frac{y}{x} - 2 \frac{x}{y}
\end{aligned}
$$