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min of (a^2+2b^2+4c^2)/ b(a+2c) for a,b,c>0

Source: 2015 Swedish Mathematical Competition p3

April 30, 2021

algebramininequalities

Problem Statement

Let

a

b

c

be positive real numbers. Determine the minimum value of the following expression

\frac{a^2+2b^2+4c^2}{b(a+2c)}