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2018 USAMO Problems/Problem 1

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Problem 1

Let $a,b,c$ be positive real numbers such that $a+b+c=4\sqrt[3]{abc}$ . Prove that $2(ab+bc+ca)+4\min(a^2,b^2,c^2)\ge a^2+b^2+c^2.$

Solution

$\textbf{Note: This is the same problem as 2018 USAJMO Problem 2.}$

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