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$(x+17)^2+(2x+16)^2+(3x+15)^2+\ldots+(16x+2)^2+(17x+1)^2=0$

If $\alpha$ and $\beta$ are the roots of the equation above, and suppose $| \alpha + \beta - \alpha \beta | = \frac a b$ for coprime positive integers $a,b$, find the value of $a+b$.

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