AUSTRIAN-POLISH 2001 Problem 2

Let $n$ be a positive integer greater than $2$ . Solve in nonnegative real numbers the following system of equations $$x_{k}+x_{k+1}=x_{k+2}^{2} , k=1,2,\cdots,n$$ where $x_{n+1}=x_{1}$ and $x_{n+2}=x_{2}$ .