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1<\frac{b}{ab+b+1}+\frac{c}{bc+c+1}+\frac{d}{cd+d+1}+\frac{a}{da+a+1}<2

Source: KJMO 2009 p6

May 2, 2019
inequalitiesalgebrafour variablesInequality

Problem Statement

If positive reals a,b,c,da,b,c,d satisfy abcd=1.abcd = 1. Prove the following inequality 1<bab+b+1+cbc+c+1+dcd+d+1+ada+a+1<2.1<\frac{b}{ab+b+1}+\frac{c}{bc+c+1}+\frac{d}{cd+d+1}+\frac{a}{da+a+1}<2.
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