Question 76
If $a, b, c \gt 0$, show that
$$
\frac{a}{\sqrt{(a+2b)^3}} + \frac{b}{\sqrt{(b+2c)^3}} + \frac{c}{\sqrt{(c+2a)^3}} \geq \frac{1}{\sqrt{a+b+c}}.
$$
$$
\frac{a}{\sqrt{(a+2b)^3}} + \frac{b}{\sqrt{(b+2c)^3}} + \frac{c}{\sqrt{(c+2a)^3}} \geq \frac{1}{\sqrt{a+b+c}}.
$$