A Shifted Radical Constraint

★ 7/10algebra Estimation Cauchy-Schwarz inequality

Problem

Let $a, b > 0$ with

a + \sqrt{b^2 + 8} = 4.

Find the minimum value of $\dfrac{3}{a} + \dfrac{1}{b}$ .

Answer

Solution

Difficulty	7/10
Topics	algebra, Estimation, Cauchy-Schwarz, inequality

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