The equation
(x−1)(x−2)(x−4)(x−5)(x−7)(x−8)=(x−3)(x−6)(x−9)
has distinct roots r1,r2,...,r6. Evaluate
6∑i=1(ri−1)(ri−2)(ri−4)
I couldn't see a neat way of doing this analytically, so I used a numerical approach:
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