inequalities: x^2 y + y^2 z + z^2 x <= 4/27 if x + y + z = 1
Source: CMO (Canada MO) 1999, problem 5
August 5, 2003
algebrainequalitiesthree variable inequalitycalculusCanada
Problem Statement
Let , , and be non-negative real numbers satisfying x \plus{} y \plus{} z \equal{} 1. Show that
x^2 y \plus{} y^2 z \plus{} z^2 x \leq \frac {4}{27}
and find when equality occurs.