TR-MO 2013 Problem 5

Tüm $a$ , $b$ , $c$ pozitif gerçel sayıları için,

$a^3 + b^3 + c^3 - 3abc \geq M(ab^2 + bc^2 + ca^2 - 3abc)$

olmasını sağlayan en büyük $M$ gerçel sayısını belirleyiniz.

Official text Turkish Mathematical Olympiad 2013 official paper, page 2. Quoted with source.

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