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Maximum of m(a,b)

Source: Bundeswettbewerb Mathematik 2009 Round 1

July 29, 2018
algebraalgebra unsolved

Problem Statement

Let a,ba,b be positive real numbers. Define m(a,b)m(a,b) as the minimum of $ a,\frac{1}{b} \text{ and } \frac{1}{a}+b.Findthemaximumof Find the maximum of m(a,b).$
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