Question 50
Let $x$ and $y$ be real numbers. Set
$$
M=\max \{x y+1, x y-x-y+3,-2 x y+x+y+2\} .
$$
Prove that $M \geqslant 2$ and determine the equality cases.
$$
M=\max \{x y+1, x y-x-y+3,-2 x y+x+y+2\} .
$$
Prove that $M \geqslant 2$ and determine the equality cases.