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(a+b+c+d)^2 > 8(ac+bd) if b < c < d

Source: Norwegian Mathematical Olympiad 1993 - Abel Competition p2

February 11, 2020
inequalitiesalgebra

Problem Statement

If a,b,c,da,b,c,d are real numbers with b<c<db < c < d, prove that (a+b+c+d)2>8(ac+bd)(a+b+c+d)^2 > 8(ac+bd).
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