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USAMO 2018 (Problem 1)

Let a,b,ca, b, c be positive real numbers such that a+b+c=4abc3a + b + c = 4\sqrt[3]{abc}. Prove that 2(ab+bc+ca)+4min⁡(a2,b2,c2)≥a2+b2+c22(ab + bc + ca) + 4\min(a^2, b^2, c^2) \ge a^2 + b^2 + c^2.