Maximizing $ab$ on a Curve

★ 6/10trigonometry Substitution algebra AM-GM inequality

Problem

Real numbers $a, b$ satisfy

\sqrt{1 - \frac{a^2}{2}} + \sqrt{1 - \frac{b^2}{3}} = \frac{3}{2}.

Find the maximum value of $ab$ .

Answer

Solution

Difficulty	6/10
Topics	trigonometry, Substitution, algebra, AM-GM, inequality

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