PL-OM 2004 Problem 4

Let real numbers $a,b,c$ . Prove that $\sqrt{2(a^2+b^2)}+\sqrt{2(b^2+c^2)}+\sqrt{2(c^2+a^2)}\ge \sqrt{3(a+b)^2+3(b+c)^2+3(c+a)^2}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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