Question 173
Determine all triples $(x, y, z)$ of non-negative real numbers that satisfy the system of equations
$$
\begin{aligned}
& x^{2}-y=(z-1)^{2} \\
& y^{2}-z=(x-1)^{2} \\
& z^{2}-x=(y-1)^{2}
\end{aligned}
$$
$$
\begin{aligned}
& x^{2}-y=(z-1)^{2} \\
& y^{2}-z=(x-1)^{2} \\
& z^{2}-x=(y-1)^{2}
\end{aligned}
$$