Question 123
If $x, y, z \in \mathbb{R}$ satisfy the nonlinear system of equations
$$
\left| \begin{array}{l} x - y + z - 1 = 0 \\ xy + 2z^2 - 6z + 1 = 0 \end{array} \right. ,
$$
find the maximum of $(x-1)^2 + (y+1)^2$.
$$
\left| \begin{array}{l} x - y + z - 1 = 0 \\ xy + 2z^2 - 6z + 1 = 0 \end{array} \right. ,
$$
find the maximum of $(x-1)^2 + (y+1)^2$.