ELMO SL 2012 A6

Let $a,b,c\ge0$ . Show that $(a^2+2bc)^{2012}+(b^2+2ca)^{2012}+(c^2+2ab)^{2012}\le (a^2+b^2+c^2)^{2012}+2(ab+bc+ca)^{2012}$ .

Calvin Deng.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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