Question 142
a, b, c are positive and $abc = 1$. Prove that
$$
\sqrt{\frac{a}{a+8}} + \sqrt{\frac{b}{b+8}} + \sqrt{\frac{c}{c+8}} \ge 1.
$$
(proposed by B. Ganbileg and U. Batzorig, inspired by Algebraic inequality book)
$$
\sqrt{\frac{a}{a+8}} + \sqrt{\frac{b}{b+8}} + \sqrt{\frac{c}{c+8}} \ge 1.
$$
(proposed by B. Ganbileg and U. Batzorig, inspired by Algebraic inequality book)