TH-TMO 2008 Problem 4

Prove that $\sqrt{a^2 + b^2 -\sqrt2 ab} +\sqrt{b^2 + c^2 -\sqrt2 bc} \ge \sqrt{a^2 + c^2}$ for all real numbers $a, b, c > 0$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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