Find the minimum (try not to use Calculus)
Source: Brazilian Math Olympiad 2008, Problem 3
October 28, 2008
calculusinequalitiestrigonometryinequalities unsolved
Problem Statement
Let real numbers such that x \plus{} y \plus{} z \equal{} xy \plus{} yz \plus{} zx. Find the minimum value of
{x \over x^2 \plus{} 1} \plus{} {y\over y^2 \plus{} 1} \plus{} {z\over z^2 \plus{} 1}