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Minimizing simple sum of fractions

Source: ISL 2020 A3

July 20, 2021
algebraInequalityIMO ShortlistIMO Shortlist 20204-variable inequalityinequalities

Problem Statement

Suppose that a,b,c,da,b,c,d are positive real numbers satisfying (a+c)(b+d)=ac+bd(a+c)(b+d)=ac+bd. Find the smallest possible value of ab+bc+cd+da.\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}. Israel
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