Question 49
Given an integer $n \ge 3$, find the maximum real number $M$, such that for any positive numbers $x_1, x_2, \dots, x_n$, there exists a permutation $y_1, y_2, \dots, y_n$ of $x_1, x_2, \dots, x_n$ that satisfies
$$
\sum_{i=1}^{n} \frac{y_i^2}{y_{i+1}^2 - y_{i+1} y_{i+2} + y_{i+2}^2} \ge M,
$$
where $y_{n+1} = y_1$, $y_{n+2} = y_2$. (posed by Qu Zhenhua)
$$
\sum_{i=1}^{n} \frac{y_i^2}{y_{i+1}^2 - y_{i+1} y_{i+2} + y_{i+2}^2} \ge M,
$$
where $y_{n+1} = y_1$, $y_{n+2} = y_2$. (posed by Qu Zhenhua)