# The importance of discriminant (2)

Algebra Level 3

$\large a \diamond b = \frac{\sqrt{a^2+4ab+b^2-2a-2b+9}}{ab+6}$

If $$(( \cdots (2017 \diamond 2016) \diamond 2015) \diamond \cdots \diamond 2) \diamond 1) = \dfrac{\sqrt{c}}{d}$$, where $$c$$ and $$d$$ are square-free positive integers , find $$c+d$$.

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