olymmath

ISL 2006 A5

    Let a,b,ca, b, c be the sides of a triangle. Prove that b+c−ab+c−a+c+a−bc+a−b+a+b−ca+b−c≤3.\frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}+\frac{\sqrt{c+a-b}}{\sqrt{c}+\sqrt{a}-\sqrt{b}}+\frac{\sqrt{a+b-c}}{\sqrt{a}+\sqrt{b}-\sqrt{c}} \leq 3 . (Korea)

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

    Official text: IMO 2006 Shortlist booklet, page 16.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

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