Question 43
Let $a$, $b$, $c$ be positive numbers such that $a$, $b$, $c \gt 1$ and
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 2.
$$
Prove that $\sqrt{a+b+c} \ge \sqrt{a-1} + \sqrt{b-1} + \sqrt{c-1}$.
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 2.
$$
Prove that $\sqrt{a+b+c} \ge \sqrt{a-1} + \sqrt{b-1} + \sqrt{c-1}$.