MathDB

3

Part of 2009 Greece National Olympiad

Problems(1)

greek mathematical olympiad 2009

Source: 3rd problem

2/24/2009
Let x,y,z x,y,z 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?
calculusinequalitiesinequalities proposed