Question 112
Let $n \ge 4$ be an integer and $x_1, x_2, \dots, x_n, x_{n+1}, x_{n+2}$ are reals, such that $x_{n+1} = x_1$ and $x_{n+2} = x_2$. Given that there exists a positive real $a$, such that $x_i^2 = a + x_{i+1}x_{i+2}$ for all $i = 1, 2, \dots, n$. Prove that at least two of the numbers $x_1, x_2, \dots, x_n$ are negative.