Question

Let $\alpha, \beta$ be the roots of the equation $x^2 - \sqrt{6}x + 3 = 0$ such that $\operatorname{Im}(\alpha) > \operatorname{Im}(\beta)$. Let $a, b$ be integers not divisible by 3 and $n$ be a natural number such that$\frac{\alpha^{99}}{\beta} + \alpha^{98} = 3^n (a + ib), i = \sqrt{-1}.$Then $n + a + b$ is equal to ______.

Answer 1

The Correct Answer is