Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

Let $\mathrm{a}>0$ be a root of the equation $2 x^2+x-2=0$. If \lim _\limits{x \rightarrow \frac{1}{a}} \frac{16\left(1-\cos \left(2+x-2 x^2\right)\right)}{(1-a x)^2}=\alpha+\beta \sqrt{17}, where $\alpha, \beta \in Z$, then $\alpha+\beta$ is equal to _________.