1. The solution set of the inequality $(x-1) \sqrt{x^{2}-x-2} \geqslant 0$ is
1. $\{-1\} \cup\{x \mid x \geqslant 2\}$.

From the problem, we get $\left\{\begin{array}{l}x-1 \geqslant 0 \\ x^{2}-x-2 \geqslant 0\end{array}\right.$ or $\left\{\begin{array}{l}x-1<0 \\ x^{2}-x-2=0,\end{array}\right.$ solving these gives $x \geqslant 2$ or $x=-1$.