olymmath

ISL 2006 A6

  • Answer

Determine the smallest number MM such that the inequality ∣ab(a2−b2)+bc(b2−c2)+ca(c2−a2)∣≤M(a2+b2+c2)2\left|a b\left(a^{2}-b^{2}\right)+b c\left(b^{2}-c^{2}\right)+c a\left(c^{2}-a^{2}\right)\right| \leq M\left(a^{2}+b^{2}+c^{2}\right)^{2} holds for all real numbers a,b,ca, b, c. (Ireland)

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

Official text: IMO 2006 Shortlist booklet, page 18.

Show the answer

\frac{9}{32} \sqrt{2}

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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