If $a,b,c,d$ are real numbers with $b < c < d$, prove that $(a+b+c+d)^2 > 8(ac+bd)$.
Problem
Source: Norwegian Mathematical Olympiad 1993 - Abel Competition p2
Tags: inequalities, algebra
Source: Norwegian Mathematical Olympiad 1993 - Abel Competition p2
Tags: inequalities, algebra
If $a,b,c,d$ are real numbers with $b < c < d$, prove that $(a+b+c+d)^2 > 8(ac+bd)$.