A four variable inequality
Source: Balkan MO ShortList 2008 A7
April 6, 2020
Problem Statement
Let . 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.