MathDB

Too easy to be in a mathematical competition surely...

Source: Pan African Olympiad 2008

October 1, 2011

inequalitiesrearrangement inequalityinequalities proposed

Problem Statement

Let

x

and

y

be two positive reals. Prove that

xy\le\frac{x^{n+2}+y^{n+2}}{x^n+y^n}

for all non-negative integers

n