Problem

Source: Kazakhstan MO 2018 final round.Grade 11;Problem 4

Tags: inequalities, algebra, analysis, Kazakhstan



Prove that for all reas $a,b,c,d\in(0,1)$ we have $$\left(ab-cd\right)\left(ac+bd\right)\left(ad-bc\right)+\min{\left(a,b,c,d\right)} < 1.$$