Problem

Source: Indonesia IMO 2010 TST, Stage 1, Test 1, Problem 1

Tags: inequalities, inequalities proposed



Let $ a$, $ b$, and $ c$ be non-negative real numbers and let $ x$, $ y$, and $ z$ be positive real numbers such that $ a+b+c=x+y+z$. Prove that \[ \dfrac{a^3}{x^2}+\dfrac{b^3}{y^2}+\dfrac{c^3}{z^2} \ge a+b+c.\] Hery Susanto, Malang