Question 105
Show that
$$
\sum_{i=1}^{n} \frac{a_i}{\sqrt{a_i^4 + 3}} \le \frac{1}{2} \sum_{i=1}^{n} \frac{1}{a_i}
$$
for all positive integers $n$ and positive real numbers $a_1, a_2, \dots, a_n$ satisfying the condition $a_1 a_2 \cdots a_n = 1$.
$$
\sum_{i=1}^{n} \frac{a_i}{\sqrt{a_i^4 + 3}} \le \frac{1}{2} \sum_{i=1}^{n} \frac{1}{a_i}
$$
for all positive integers $n$ and positive real numbers $a_1, a_2, \dots, a_n$ satisfying the condition $a_1 a_2 \cdots a_n = 1$.