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inequality, p1

Source: Turkey National Mathematical Olympiad 2019 P1

December 22, 2019
inequalitiesturkey MO 2019 p1

Problem Statement

a,b,ca, b, c are positive real numbers such that (ab−1)(bc−1)(ca−1)=1(\sqrt {ab}-1)(\sqrt {bc}-1)(\sqrt {ca}-1)=1 At most, how many of the numbers: a−bc,a−cb,b−ac,b−ca,c−ab,c−baa-\frac {b}{c}, a-\frac {c}{b}, b-\frac {a}{c}, b-\frac {c}{a}, c-\frac {a}{b}, c-\frac {b}{a} can be bigger than 11?
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