For non-negative numbers $x$ and $y$ not exceeding $1$, prove that $$\frac{1}{\sqrt{1+x^2}}+\frac{1}{\sqrt{1+y^2}} \le \frac{2}{\sqrt{1 + xy}},$$
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Tags: algebra, inequalities
For non-negative numbers $x$ and $y$ not exceeding $1$, prove that $$\frac{1}{\sqrt{1+x^2}}+\frac{1}{\sqrt{1+y^2}} \le \frac{2}{\sqrt{1 + xy}},$$