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The equation

\((x-1)(x-2)(x-4)(x-5)(x-7)(x-8)=(x-3)(x-6)(x-9)\)

has distinct roots \(r_1,r_2,...,r_6\). Evaluate 

\(\displaystyle\sum_{i=1}^{6}(r_i-1)(r_i-2)(r_i-4)\)

 Feb 27, 2024
 #1
avatar+33616 
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I couldn't see a neat way of doing this analytically, so I used a numerical approach:

 

 Feb 29, 2024

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