MathDB

1/(1-a)+ 1/(1-b) >= 4 if a,b>0 with a^2 + b^2 =1/2

Source: 2022 Austrian Regional Competition For Advanced Students p1

October 4, 2022

algebrainequalities

Problem Statement

Let

a

and

b

be positive real numbers with

a^2 + b^2 =\frac12

. Prove that

\frac{1}{1 - a}+\frac{1}{1-b}\ge 4.

When does equality hold?
(Walther Janous)