Find the largest K
Source: Iranian National Olympiad (3rd Round) 2008
August 30, 2008
functioninequalitiesinequalities proposed
Problem Statement
Find the smallest real such that for each x,y,z\in\mathbb R^{ \plus{} }:
x\sqrt y \plus{} y\sqrt z \plus{} z\sqrt x\leq K\sqrt {(x \plus{} y)(y \plus{} z)(z \plus{} x)}