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question5

Source: iran tst 2014 first exam

April 14, 2014
inequalitiesfunctioninequalities unsolvedn-variable inequality

Problem Statement

nn is a natural number. for every positive real numbers x1,x2,...,xn+1x_{1},x_{2},...,x_{n+1} such that x1x2...xn+1=1x_{1}x_{2}...x_{n+1}=1 prove that: nx1+...+nxn+1≥nx1n+...+nxn+1n\sqrt[x_{1}]{n}+...+\sqrt[x_{n+1}]{n} \geq n^{\sqrt[n]{x_{1}}}+...+n^{\sqrt[n]{x_{n+1}}}
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