Inequality with x+y+z=1
Source: China TST 2006
June 18, 2006
inequalitiesfunction
Problem Statement
Given three positive real numbers , , such that x \plus{} y \plus{} z \equal{} 1, prove that
\frac {xy}{\sqrt {xy \plus{} yz}} \plus{} \frac {yz}{\sqrt {yz \plus{} zx}} \plus{} \frac {zx}{\sqrt {zx \plus{} xy}} \le \frac {\sqrt {2}}{2}.