Problem

Source: ELMO 2014 Shortlist A3, by Allen Liu

Tags: inequalities, parameterization, inequalities proposed



Let $a,b,c,d,e,f$ be positive real numbers. Given that $def+de+ef+fd=4$, show that \[ ((a+b)de+(b+c)ef+(c+a)fd)^2 \geq\ 12(abde+bcef+cafd). \]Proposed by Allen Liu