Question 61
Let $a, b, c, d$ be positive numbers such that $abcd = 1$. Prove the inequality
$$
\frac{1}{\sqrt{a + 2b + 3c + 10}} + \frac{1}{\sqrt{b + 2c + 3d + 10}} + \frac{1}{\sqrt{c + 2d + 3a + 10}} + \frac{1}{\sqrt{d + 2a + 3b + 10}} \le 1.
$$
$$
\frac{1}{\sqrt{a + 2b + 3c + 10}} + \frac{1}{\sqrt{b + 2c + 3d + 10}} + \frac{1}{\sqrt{c + 2d + 3a + 10}} + \frac{1}{\sqrt{d + 2a + 3b + 10}} \le 1.
$$