A Ten-Sum Constraint

★ 7/10Substitution algebra Cauchy-Schwarz AM-GM inequality

Problem

Positive reals $a, b$ satisfy

a + b + \frac{1}{a} + \frac{9}{b} = 10.

Find the range of possible values of $a + b$ .

Answer

Solution

Difficulty	7/10
Topics	Substitution, algebra, Cauchy-Schwarz, AM-GM, inequality

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