Question 50
Find all triples $(x, y, z)$ of real numbers that satisfy
$$
\begin{cases}
\frac{x}{y} + \frac{y}{z} + xy = 3, \\
\frac{y}{z} + \frac{z}{x} + yz = 3, \\
\frac{z}{x} + \frac{x}{y} + zx = 3.
\end{cases}
$$
$$
\begin{cases}
\frac{x}{y} + \frac{y}{z} + xy = 3, \\
\frac{y}{z} + \frac{z}{x} + yz = 3, \\
\frac{z}{x} + \frac{x}{y} + zx = 3.
\end{cases}
$$