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Let a, b, c be positive real numbers such that \frac{a}{1+a}+\frac{b}{1+b}+\frac{c}{1+c}=2\text{.}
Prove that \frac{\sqrt a + \sqrt b+\sqrt c}{2} \geq \frac{1}{\sqrt a}+\frac{1}{\sqrt b}+\frac{1}{\sqrt c}\text{.}

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