Question 174
Determine all real numbers $a$ for which there exists an infinite sequence of strictly positive real numbers $x_{0}, x_{1}, x_{2}, x_{3}, \ldots$ satisfying, for every $n$, the equality
$$
x_{n+2}=\sqrt{a x_{n+1}-x_{n}} .
$$
$$
x_{n+2}=\sqrt{a x_{n+1}-x_{n}} .
$$