Inequality 3 variables - seems familiar
Source: Hungary-Israel Binational Olympiad 2009, Problem 5
August 17, 2009
inequalitiesquadratics
Problem Statement
Let , and be non negative numbers. Prove that \frac{x^2\plus{}y^2\plus{}z^2\plus{}xy\plus{}yz\plus{}zx}{6}\le \frac{x\plus{}y\plus{}z}{3}\cdot\sqrt{\frac{x^2\plus{}y^2\plus{}z^2}{3}}