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minimum of \sqrt{\frac{a}{b(3a+2)}}+\sqrt{\frac{b}{a(3b+2)}}

Source: JBMO Shortlist 2017 A2

July 25, 2018

algebraminimum valueJBMO

Problem Statement

Let

a

and

b

be positive real numbers such that

3a^2 + 2b^2 = 3a + 2b

. Find the minimum value of

A =\sqrt{\frac{a}{b(3a+2)}} + \sqrt{\frac{b}{a(2b+3)}}