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★ 8/10Substitution algebra Estimation inequality

Problem

Let $a, b, m > 0$ . The inequality

\sqrt{\frac{a^2}{a^2+b^2}} + m\sqrt{\frac{b}{a+b}} \le \frac{5\sqrt2}{2}

holds for all $a, b > 0$ . Find the maximum value of $m$ .

Answer

Solution

Difficulty	8/10
Topics	Substitution, algebra, Estimation, inequality

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