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(2^x +3^x)/(3^x +4^x)<=5/7 if x>=1 (I Soros Olympiad 1994-95 R1 11.1)

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July 31, 2021
algebrainequalities

Problem Statement

Prove that for real x≥1x\ge 1, holds the inequality 2x+3x3x+4x≤57\frac{2^x +3^x }{3^x +4^x} \le \frac57
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