Question 38
Suppose that $x$, $y$ and $z$ are positive real numbers and $x^2 + y^2 + z^2 = x^2 y^2 + y^2 z^2 + z^2 x^2$. Prove that
$$
(x - y)^2 (y - z)^2 (z - x)^2 \le (x^2 - y^2)^2 + (y^2 - z^2)^2 + (z^2 - x^2)^2.
$$
$$
(x - y)^2 (y - z)^2 (z - x)^2 \le (x^2 - y^2)^2 + (y^2 - z^2)^2 + (z^2 - x^2)^2.
$$