IMO 1992 LL POL57

For positive numbers a, b, c define A = (a + b + c)/3, G =

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IMO 1992 LL POL57

Origin: POL

Problem

For positive numbers a, b, c define A = (a + b + c)/3, G = (abc)1/3, H = 3/(a−1 + b−1 + c−1). Prove that A G 3 \geq1 4 + 3 4 \cdot A H , for every a, b, c > 0.