MathDB

Romania District Olympiad 2010

Source: Grade X

March 13, 2010

inequalities proposedinequalities

Problem Statement

Consider two real numbers

a\in [ - 2,\infty)\ ,\ r\in [0,\infty)

and the natural number

n\ge 1

. Show that:

r^{2n} + ar^n + 1\ge (1 - r)^{2n}