Question 74
If $n \in \mathbb{N}^*$ and $x_0 \lt x_1 \lt x_2 \lt \dots \lt x_n$ are real numbers, show that
$$
2x_n + \frac{1}{(x_1 - x_0)^2} + \frac{1}{(x_2 - x_1)^2} + \dots + \frac{1}{(x_n - x_{n-1})^2} \ge 3n + 2x_0.
$$
$$
2x_n + \frac{1}{(x_1 - x_0)^2} + \frac{1}{(x_2 - x_1)^2} + \dots + \frac{1}{(x_n - x_{n-1})^2} \ge 3n + 2x_0.
$$