A Two-Variable Radical Bound

Problem

For $0 \le x, y \le 1$ , prove that

\frac{1}{\sqrt{1+x^2}} + \frac{1}{\sqrt{1+y^2}} \le \frac{2}{\sqrt{1+xy}}.

Answer

Solution

Difficulty	8/10
Topics	AM-GM, inequality, Symmetry

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