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JEE Main 2024

05-04-2024 S2

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

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