Maths Olympiad Prep

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Algebra Difficulty 6.3 National olympiad Find the answer

Example 17 (47th IMO, Day 1 Problem 3, July 12-13, 2006, in Ljubljana, Slovenia) Find the smallest real number MM such that for all real numbers a,b,ca, b, c, 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| \leqslant M\left(a^{2}+b^{2}+c^{2}\right)^{2}
holds.

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

Translate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.

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None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.