Question 64
Solve the following system of equations
$$
\begin{cases}
\sqrt{x^2 - 2x + 6} \log_3 (6-y) = x \\
\sqrt{y^2 - 2y + 6} \log_3 (6-z) = y \\
\sqrt{z^2 - 2z + 6} \log_3 (6-x) = z.
\end{cases}
$$
$$
\begin{cases}
\sqrt{x^2 - 2x + 6} \log_3 (6-y) = x \\
\sqrt{y^2 - 2y + 6} \log_3 (6-z) = y \\
\sqrt{z^2 - 2z + 6} \log_3 (6-x) = z.
\end{cases}
$$