Let $o$, $r$, $g$, $t$, $n$, $i$, $z$, $e$, and $d$ be positive reals. Show that \[ \sqrt{(d+o+t+t+e+d)(o+r+z+i+n+g)} > \sqrt{ti} + \sqrt{go} + \sqrt[6]{orz}. \]when $d^2e \geq \tfrac{2}{1434}$. Proposed by David Fox
Source: 2024 RELMO 1 / RELSMO 1
Tags: inequalities
Let $o$, $r$, $g$, $t$, $n$, $i$, $z$, $e$, and $d$ be positive reals. Show that \[ \sqrt{(d+o+t+t+e+d)(o+r+z+i+n+g)} > \sqrt{ti} + \sqrt{go} + \sqrt[6]{orz}. \]when $d^2e \geq \tfrac{2}{1434}$. Proposed by David Fox