Solve the following system of equations, in which
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
is a given number satisfying
![|a| > 1](/media/m/b/4/7/b478ed2579aeb863ee65cb7283382af0.png)
:
%V0
Solve the following system of equations, in which $a$ is a given number satisfying $|a| > 1$:
$\begin{matrix}x_{1}^{2}= ax_{2}+1\\ x_{2}^{2}= ax_{3}+1\\ \ldots\\ x_{999}^{2}= ax_{1000}+1\\ x_{1000}^{2}= ax_{1}+1\\ \end{matrix}$