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a (1- b)>1/4 , b (1-c)>1/4 , c (1-a)>1/4 (Chile NMO 1993 P5)

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November 21, 2021
algebrainequalities

Problem Statement

Let a,b,ca,b,c three positive numbers less than 1 1. Prove that cannot occur simultaneously these three inequalities: a(1−b)>14a (1- b)>\frac14 b(1−c)>14b (1-c)>\frac14 c(1−a)>14c (1-a)>\frac14
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