Question 200
Suppose $a$, $b$, $c$ are the side lengths of a triangle. Prove that
$$
(a+b+c)(a^2+b^2+c^2) + a(b-c)^2 + b(c-a)^2 + c(a-b)^2 \le 3(a^3+b^3+c^3),
$$
with equality iff the triangle is equilateral.
$$
(a+b+c)(a^2+b^2+c^2) + a(b-c)^2 + b(c-a)^2 + c(a-b)^2 \le 3(a^3+b^3+c^3),
$$
with equality iff the triangle is equilateral.