what is the value of positive constant k?
Source: 2007 Korean MO, 2nd Round, P.M.
August 18, 2007
inequalitiesinequalities unsolved
Problem Statement
For all positive reals , , and , what is the value of positive constant satisfies the following inequality?
\frac{a}{c\plus{}kb}\plus{}\frac{b}{a\plus{}kc}\plus{}\frac{c}{b\plus{}ka}\geq\frac{1}{2007} .