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exponential inequality

Source: China south east mathematical olympiad 2004 day1 problem 1

June 29, 2013
inequalitiesinequalities unsolved

Problem Statement

Let real numbers a, b, c satisfy a2+2b2+3c2=32a^2+2b^2+3c^2= \frac{3}{2}, prove that 3−a+9−b+27−c≥13^{-a}+9^{-b}+27^{-c}\ge1.
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