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x^n + 1/x^n - 2 > n^2(x + 1/x -2)

Source: Czech - Polish - Slovak Match 2013: P2

May 24, 2014
inequalitiesinequalities proposed

Problem Statement

Prove that for every real number x>0x>0 and each integer n>0n>0 we have xn+1xn−2≥n2(x+1x−2)x^n+\frac1{x^n}-2 \ge n^2\left(x+\frac1x-2\right)
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