Interesting inequality
Source: BiH JBMO TST08 problem 1
June 1, 2008
inequalitiesinequalities proposed
Problem Statement
Let be real positive numbers such that absolute difference between any two of them is less than . Prove that: a \plus{} b \plus{} c < \sqrt {ab \plus{} 1} \plus{} \sqrt {ac \plus{} 1} \plus{} \sqrt {bc \plus{} 1}