MathDB

Triangle inequality

Source: Nigeria mo 3rd round problem 2

September 8, 2019

algebratriangle inequalityinequalities

Problem Statement

Let

abc

be real numbers satisfying

ab+bc+ca=1

. Show that

\frac{|a-b|}{|1+c^2|}

\frac{|b-c|}{|1+a^2|}

>=

\frac{|c-a|}{|1+b^2|}