Question 57
Prove the inequality
$$
\frac{a}{a + \sqrt{(a+b)(a+c)}} + \frac{b}{b + \sqrt{(b+c)(b+a)}} + \frac{c}{c + \sqrt{(c+a)(c+b)}} \le 1,
$$
in which $a$, $b$ and $c$ are assumed to be positive numbers.
$$
\frac{a}{a + \sqrt{(a+b)(a+c)}} + \frac{b}{b + \sqrt{(b+c)(b+a)}} + \frac{c}{c + \sqrt{(c+a)(c+b)}} \le 1,
$$
in which $a$, $b$ and $c$ are assumed to be positive numbers.