Question 94
Let $a$, $b$, $c$ be distinct positive real numbers. Show that
$$
\frac{(b-c)^4}{(a-b)^2(a-c)^2} + \frac{(a-c)^4}{(a-b)^2(b-c)^2} + \frac{(a-b)^4}{(a-c)^2(b-c)^2} \ge \frac{33}{2}.
$$
$$
\frac{(b-c)^4}{(a-b)^2(a-c)^2} + \frac{(a-c)^4}{(a-b)^2(b-c)^2} + \frac{(a-b)^4}{(a-c)^2(b-c)^2} \ge \frac{33}{2}.
$$