Question 4
Let $x_1, x_2, x_3$ and $x_4$ be positive real numbers. Prove the inequality:
$$
\frac{x_1 + 3x_2}{x_2 + x_3} + \frac{x_2 + 3x_3}{x_3 + x_4} + \frac{x_3 + 3x_4}{x_4 + x_1} + \frac{x_4 + 3x_1}{x_1 + x_2} \ge 8.
$$
$$
\frac{x_1 + 3x_2}{x_2 + x_3} + \frac{x_2 + 3x_3}{x_3 + x_4} + \frac{x_3 + 3x_4}{x_4 + x_1} + \frac{x_4 + 3x_1}{x_1 + x_2} \ge 8.
$$