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Indian Mathematical Olympiad 1988 - Problem 4

Source:

August 14, 2009

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Problem Statement

a

and

b

are positive and a \plus{} b \equal{} 1, prove that \left(a\plus{}\frac{1}{a}\right)^2\plus{}\left(b\plus{}\frac{1}{b}\right)^2 \geq \frac{25}{2}