Three variables cyclic inequality
Source: Moldova IMO-BMO TST 2003, day 1, problem 2.
August 14, 2008
inequalitiesLaTeXinequalities unsolved
Problem Statement
The positive reals and are satisfying the relation x \plus{} y \plus{} z\geq 1. Prove that:
\frac {x\sqrt {x}}{y \plus{} z} \plus{} \frac {y\sqrt {y}}{z \plus{} x} \plus{} \frac {z\sqrt {z}}{x \plus{} y}\geq \frac {\sqrt {3}}{2}
Proposer: Baltag Valeriu