Question 94
Let $x$, $y$, $z$ be pairwise distinct real numbers such that $x^2 - 1/y = y^2 - 1/z = z^2 - 1/x$. Given $z^2 - 1/x = a$, prove that
$$
(x+y+z)xyz = -a^2. \qquad \text{(I. Voronovich)}
$$
$$
(x+y+z)xyz = -a^2. \qquad \text{(I. Voronovich)}
$$