MathDB

Inequality with condition xyz=3(x+y+z)

Source: Balkan MO ShortList 2011 A4

April 6, 2020

inequalitiesalgebraHigh school olympiadBalkan

Problem Statement

Let

x,y,z \in \mathbb{R}^+

satisfying

xyz=3(x+y+z)

. Prove, that \begin{align*} \sum \frac{1}{x^2(y+1)} \geq \frac{3}{4(x+y+z)} \end{align*}