Question 16
Let $n$ be a positive integer.
Find all real numbers $x_{1}, x_{2}, \ldots, x_{n}$ such that
$$
\prod_{k=1}^{n}\left(x_{k}^{2}+(k+2) x_{k}+k^{2}+k+1\right)=\left(\frac{3}{4}\right)^{n}(n!)^{2}
$$
Find all real numbers $x_{1}, x_{2}, \ldots, x_{n}$ such that
$$
\prod_{k=1}^{n}\left(x_{k}^{2}+(k+2) x_{k}+k^{2}+k+1\right)=\left(\frac{3}{4}\right)^{n}(n!)^{2}
$$