Let a >0 be a root of the equation 2 x^2+x-2=0. If lim_x → 1/a (16(1- cos (2+x-2 x^2)))/((1-a x)^2)=α+β √ 17, where α, β ∈ Z, then α+β is equal to…

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