SMO 2019 Junior Round 1 Question 4

Let $x,y$ and $z$ be positive integers satisfying $$x^2+y^2+z^2=2(xy+1)\qquad\text{and}\qquad x+y+z=2022.$$ If $x_1$ and $x_2$ are two distinct solutions for $x$, what is the value of $x_1+x_2$?