Minimum Value of a Non-symmetric Expression
Source: Moldova 2008 IMO-BMO Second TST Problem 2
March 29, 2008
inequalitiesfunctioninequalities proposed
Problem Statement
Let be positive reals so that a_1\plus{}a_2\plus{}\ldots\plus{}a_n\le\frac n2. Find the minimal value of
\sqrt{a_1^2\plus{}\frac1{a_2^2}}\plus{}\sqrt{a_2^2\plus{}\frac1{a_3^2}}\plus{}\ldots\plus{}\sqrt{a_n^2\plus{}\frac1{a_1^2}}.