MathDB

1/a(a+1)+ 1/b(b+1)+1/c(c+1) >= 3/2 if abc=1 and a,b,c>0

Source: Tuymaada 2000 Juniors 4

April 28, 2019

algebrainequalitiesthree variable inequality

Problem Statement

Prove that if the product of positive numbers

a,b

and

c

equals one, then

\frac{1}{a(a+1)}+\frac{1}{b(b+1)}+\frac{1}{c(c+1)}\ge \frac{3}{2}