UZ-MO 2013 Problem 1

Let real numbers $a,b$ such that $a\ge b\ge 0$ . Prove that $\sqrt{a^2+b^2}+\sqrt[3]{a^3+b^3}+\sqrt[4]{a^4+b^4} \le 3a+b .$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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