Question 163
Let $x$, $y$, $z$ be pairwise distinct non-negative real numbers. Prove that
$$
(xy + yz + zx) \left( \frac{1}{(x-y)^2} + \frac{1}{(y-z)^2} + \frac{1}{(z-x)^2} \right) \ge 4.
$$
When does equality hold?
$$
(xy + yz + zx) \left( \frac{1}{(x-y)^2} + \frac{1}{(y-z)^2} + \frac{1}{(z-x)^2} \right) \ge 4.
$$
When does equality hold?