Question 68
Let $a$, $b$, $c \gt 0$. Prove that
$$
\sqrt[7]{\frac{a}{b+c} + \frac{b}{c+a}} + \sqrt[7]{\frac{b}{c+a} + \frac{c}{a+b}} + \sqrt[7]{\frac{c}{a+b} + \frac{a}{b+c}} \ge 3.
$$
$$
\sqrt[7]{\frac{a}{b+c} + \frac{b}{c+a}} + \sqrt[7]{\frac{b}{c+a} + \frac{c}{a+b}} + \sqrt[7]{\frac{c}{a+b} + \frac{a}{b+c}} \ge 3.
$$