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Interesting Inequality

Source: 1988 IrMO Paper 1 Problem 10

September 28, 2017
inequalities

Problem Statement

Let 0≤x≤10\le x\le 1. Show that if nn is any positive integer, then (1+x)n≥(1−x)n+2nx(1−x2)n−12(1+x)^n\ge (1-x)^n+2nx(1-x^2)^{\frac{n-1}{2}}.
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