KZ-MO 2018 Problem 4

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

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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