Roots in the Denominator

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

Problem

Let $a > 1$ and $b > 2$ . Find the minimum value of

m = \frac{(a+b)^2}{\sqrt{a^2-1} + \sqrt{b^2-4}}.

Answer

Solution

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

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