MathDB

4

Part of 2017 Iran MO (2nd Round)

Problems(1)

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

4/21/2017
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).
algebra2-variable inequalityInequalityinequalities