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Square Sum Settlement (Posted on 2015-01-14) Difficulty: 2 of 5
If x2 + x +1 =0, then find the value of:
(x+1/x)2 + (x2 + x-2)2 + ...+ (x9 + x-9)2

No Solution Yet Submitted by K Sengupta    
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re: computer solution (spoiler) | Comment 2 of 3 |
(In reply to computer solution (spoiler) by Charlie)

The behavior you noted happens because the two solutions are two of the three complex cube roots of one. 
x=cos(120)+i*sin(120) and x=cos(240)+i*sin(240).

So if you square either of them you get the other, but cubing gives 1.

  Posted by Jer on 2015-01-14 11:26:08

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