Inequality with non-trivial answer
Source: Ukraine TST 2009, problem 2
May 4, 2009
inequalitiesinequalities proposed
Problem Statement
Let , , are sides of a triangle. Find the least possible value such that the following inequality always holds:
\left|\frac{a\minus{}b}{a\plus{}b}\plus{}\frac{b\minus{}c}{b\plus{}c}\plus{}\frac{c\minus{}a}{c\plus{}a}\right|