Finding a Term in a Nonlinear Recursive Sequence

Consider a sequence $x_1, x_2, \ldots, x_{12}$ of real numbers such that $x_1 = 1$ and for $n = 1, \ldots, 10$,$$x_{n+2} = \frac{(x_{n+1}+1)(x_{n+1}-1)}{x_n}.$$Suppose $x_n > 0$ for $n = 1, \ldots, 11$ and $x_{12} = 0$. Compute $x_2$. The answer is in the form $\frac{\sqrt{a}+\sqrt{b}}{c}$ where $a$, $b$, $c$ are positive integers. Input the minimum value of $a+b+c$.