Question 37
If $ab+bc+ca = 1$ for numbers $a, b, c \gt 0$
$$
\sqrt[3]{\frac{1}{a} + 6b} + \sqrt[3]{\frac{1}{b} + 6c} + \sqrt[3]{\frac{1}{c} + 6a} \le \frac{1}{abc}
$$
confirm that.
$$
\sqrt[3]{\frac{1}{a} + 6b} + \sqrt[3]{\frac{1}{b} + 6c} + \sqrt[3]{\frac{1}{c} + 6a} \le \frac{1}{abc}
$$
confirm that.