# Inspired by Calvin Lin - Part III

Algebra Level 5

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

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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