The importance of discriminant (2)

Algebra Level 4

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

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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