MathDB

\frac{x^2}{x+y}+\frac{y^2}{1-x}+\frac{(1-x-y)^2}{1-y}\geq\frac{1}{2} if 0<x,y<1

Source: KJMO 2009 p3

May 2, 2019

algebrainequalitiesInequality

Problem Statement

For two arbitrary reals

x, y

which are larger than

0

and less than

1.

Prove that

\frac{x^2}{x+y}+\frac{y^2}{1-x}+\frac{(1-x-y)^2}{1-y}\geq\frac{1}{2}.