Question 3
Determine all triples $(x,y,z)$ of real numbers satisfying
$$
\begin{aligned}
x^2-yz&=|y-z|+1,\\
y^2-zx&=|z-x|+1,\\
z^2-xy&=|x-y|+1.
\end{aligned}
$$
$$
\begin{aligned}
x^2-yz&=|y-z|+1,\\
y^2-zx&=|z-x|+1,\\
z^2-xy&=|x-y|+1.
\end{aligned}
$$