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Prove \frac{x-y}{x^6-y^6}\leq \frac{4}{3}(x+y) if x^4-y^4=x-y

Source: Iran National Olympiad 2017, Second Round, Problem 4

April 21, 2017
algebra2-variable inequalityInequalityinequalities

Problem Statement

Let x,yx,y be two positive real numbers such that x4−y4=x−yx^4-y^4=x-y. Prove that x−yx6−y6≤43(x+y).\frac{x-y}{x^6-y^6}\leq \frac{4}{3}(x+y).
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