Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $$\sqrt{\frac{a+b}{b+1}}+\sqrt{\frac{b+c}{c+1}}+\sqrt{\frac{c+a}{a+1}} \ge 3$$
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Tags: inequalities, 6th edition
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $$\sqrt{\frac{a+b}{b+1}}+\sqrt{\frac{b+c}{c+1}}+\sqrt{\frac{c+a}{a+1}} \ge 3$$