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min of S = 2a +3 +32/(a - b) (2b +3)^2, for a>b>0 (HOMC 2019 JI-9)

Source:

November 7, 2020

algebrainequalitiesmin

Problem Statement

Let

a

and

b

be positive real numbers with

a > b

. Find the smallest possible values of

S = 2a +3 +\frac{32}{(a - b)(2b +3)^2}