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a^n +1a^n -2 >= n^2 (a +1/a -2 )

Source: Switzerland - Swiss TST 2002 p9

February 18, 2020
inequalitiesalgebra

Problem Statement

For each real number aa and integer n≥1n \ge 1 prove the inequality an+1an−2≥n2(a+1a−2)a^n +\frac{1}{a^n} -2 \ge n^2 \left(a +\frac{1}{a} -2\right) and find the cases of equality.
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