International Mathematical Olympiad 1983 Problem 6

AlgebraInequalitiesTriangle

Let aa, bb and cc be the lengths of the sides of a triangle. Prove that a2b(a−b)+b2c(b−c)+c2a(c−a)≥0.a^2b(a - b) + b^2c(b - c) + c^2a(c - a) \geq 0.

Determine when equality occurs.