GAIC Math 2024 Problem 59

Let $x_0>0, x_0 \neq \sqrt{3}, Q(x_0,0), P(0,4)$, and the line PQ intersects the hyperbola $x^2-\frac{y^2}{3}=1$ at points A and B. If $\overrightarrow{PQ}=t\overrightarrow{QA}=(2-t)\overrightarrow{QB}$, then $x_0=\_\_\_\_\_$.