Question 37
Let $x_{i} \gt 1$, for all $i \in \{1,2,3, \ldots, 2011\}$. Prove the inequality
$$
\sum_{i=1}^{2011} \frac{x_{i}^{2}}{x_{i+1}-1} \geq 8044
$$
where $x_{2012} = x_{1}$. When does equality hold?
$$
\sum_{i=1}^{2011} \frac{x_{i}^{2}}{x_{i+1}-1} \geq 8044
$$
where $x_{2012} = x_{1}$. When does equality hold?