A Product of Radicals

★ 7/10Substitution algebra AM-GM inequality

Problem

Let $x, y \geqslant 0$ with $(1 + x)(1 + y) = 2$ . Prove that

\sqrt{1 + x^2}\cdot\sqrt{1 + y^2} \geqslant 4 - 2\sqrt{2}.

Answer

Solution

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

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