INMO 2007 Problem 6
Source: Inequality
February 4, 2007
geometryinequalitiestrigonometryLaTeXinradiuscircumcircleincenter
Problem Statement
If , , are positive real numbers, prove that
\left(x \plus{} y \plus{} z\right)^2 \left(yz \plus{} zx \plus{} xy\right)^2 \leq 3\left(y^2 \plus{} yz \plus{} z^2\right)\left(z^2 \plus{} zx \plus{} x^2\right)\left(x^2 \plus{} xy \plus{} y^2\right) .