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Berkeley Math Circle

Algebra Difficulty 4.7 AIME Prove it United States

Problem:
Show that for all real numbers $a, b, c$ ,
$a^{6} + b^{6} + c^{6} - 3 a^{2} b^{2} c^{2} \geq \frac{1}{2}(a-b)^{2}(b-c)^{2}(c-a)^{2}$

Solution

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