0733
Source:
May 12, 2008
inequalitiesfunctionlimit
Problem Statement
Find the greatest positive real number such that the inequality below holds for any positive real numbers :
\frac ab \plus{} \frac bc \plus{} \frac ca \minus{} 3 \geq k \left( \frac a{b \plus{} c} \plus{} \frac b{c \plus{} a} \plus{} \frac c{a \plus{} b} \minus{} \frac 32 \right).