Let , be the roots of the equation x^2-√6x+3=0 such that Im()Im().

Question

Let $\alpha,\beta$ be the roots of the equation $x^2-\sqrt6x+3=0$ 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 [a stated relation among $\alpha,\beta,a,b,n$]. Then $n+a+b$ is equal to \_\_\_\_

Answer: 49

Accepted Answer

*(The governing relation between $\alpha,\beta,a,b,n$ was not preserved in the extracted source text, so the derivation could not be reliably reconstructed. The final numeric answer, 49, is preserved from the source.)*

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