1. Let $\frac{\pi}{2}<\alpha<\pi$, then the range of real numbers $x$ that satisfy the equation $\sin \alpha-\sqrt{3} \cos \alpha=\log _{2}\left(x^{2}-x+2\right)$ is $\qquad$ .
1. $\{x \mid-1 \leqslant x<0$ or $1<x \leqslant 2\}$ Detailed explanation: The range on the left side of the equation is $(1,2]$, solving for the range of $x$ yields $\{x \mid-1 \leqslant x<0$ or $1<x \leqslant 2\}$.