MathDB

A7

Part of 2008 Balkan MO Shortlist

Problems(1)

A four variable inequality

Source: Balkan MO ShortList 2008 A7

4/6/2020
Let x,y,z,t∈R≥0x,y,z,t \in \mathbb{R}_{\geq 0}. Show \begin{align*} \sqrt{xy}+\sqrt{xz}+\sqrt{xt}+\sqrt{yz}+\sqrt{yt}+\sqrt{zt} \geq 3 \sqrt[3]{xyz+xyt+xzt+yzt} \end{align*} and determine the equality cases.