Question 1
Solve the system
$$\begin{cases}\sqrt{x^2-2x+6}\,\log_3(6-y)=x,\\ \sqrt{y^2-2y+6}\,\log_3(6-z)=y,\\ \sqrt{z^2-2z+6}\,\log_3(6-x)=z.\end{cases}$$
$$\begin{cases}\sqrt{x^2-2x+6}\,\log_3(6-y)=x,\\ \sqrt{y^2-2y+6}\,\log_3(6-z)=y,\\ \sqrt{z^2-2z+6}\,\log_3(6-x)=z.\end{cases}$$