Lovely inequality [Walther Janous's problem from 1989]
Source: Jack Garfunkel, P1490, CRUX 1989/9, p.270, Chinese TST 2007 5th quiz P3
November 7, 2003
inequalities3-variable inequalitycyclic inequalitysquare root inequality
Problem Statement
Find the smallest constant such that
\frac {x}{\sqrt {x \plus{} y}} \plus{} \frac {y}{\sqrt {y \plus{} z}} \plus{} \frac {z}{\sqrt {z \plus{} x}}\leq k\sqrt {x \plus{} y \plus{} z}
for all positive , , .