Inequality for sides of a triangle a,b,c
Source: Romanian TST 2001
January 16, 2011
inequalitiesinequalities proposed
Problem Statement
The sides of a triangle have lengths . Prove that:
\begin{align*}(-a+b+c)(a-b+c)\, +\, & (a-b+c)(a+b-c)+(a+b-c)(-a+b+c)\\ &\le\sqrt{abc}(\sqrt{a}+\sqrt{b}+\sqrt{c})\end{align*}