Question 56
Determine all triples $(x, y, z)$ of real numbers satisfying:
$$
\begin{aligned}
x^2 - yz &= |y - z| + 1, \\
y^2 - zx &= |z - x| + 1, \\
z^2 - xy &= |x - y| + 1.
\end{aligned}
$$
$$
\begin{aligned}
x^2 - yz &= |y - z| + 1, \\
y^2 - zx &= |z - x| + 1, \\
z^2 - xy &= |x - y| + 1.
\end{aligned}
$$