MathDB
Inequality involving x, y and z

Source: Balkan MO 2012 - Problem 2

April 28, 2012
functiontrigonometrytriangle inequalityrearrangement inequalityBalkan

Problem Statement

Prove that ∑cyc(x+y)(z+x)(z+y)≥4(xy+yz+zx),\sum_{cyc}(x+y)\sqrt{(z+x)(z+y)} \geq 4(xy+yz+zx), for all positive real numbers x,yx,y and zz.
Back to ProblemsView on AoPS