greek mathematical olympiad 2009
Source: 3rd problem
February 24, 2009
calculusinequalitiesinequalities proposed
Problem Statement
Let be nonnegative real numbers such that x \plus{} y \plus{} z \equal{} 2. Prove that x^{2}y^{2} \plus{} y^{2}z^{2} \plus{} z^{2}x^{2} \plus{} xyz\leq 1. When does the equality occur?