olymmath

ISL 2008 A5

    Let a,b,c,da, b, c, d be positive real numbers such that abcd=1 and a+b+c+d>ab+bc+cd+daa b c d=1 \text { and } a+b+c+d>\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a} Prove that a+b+c+d<ba+cb+dc+ada+b+c+d<\frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}

    Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

    Official text: IMO 2008 Shortlist booklet, page 15.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

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