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 Square Sum Settlement (Posted on 2015-01-14)
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 No Rating

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 computer solution (spoiler) | Comment 1 of 3
list
10   for Disc=-1 to 1 step 2
20    X=(-1+Disc*sqrt(1-4))/2
25    Tot=0
30    for I=1 to 9
40       Tot=Tot+(X^I+1/X^I)^2
45       print (X^I+1/X^I)
50    next
60    print Tot:print
70   next
OK
run
-1.0
-1.0-0.0000000000000000001#i
2.0
-1.0+0.0000000000000000003#i
-1.0-0.0000000000000000004#i
2.0
-1.0+0.0000000000000000006#i
-1.0-0.0000000000000000008#i
2.0
17.9999999999999999997+0.0000000000000000005#i

-1.0
-1.0+0.0000000000000000001#i
2.0
-1.0-0.0000000000000000003#i
-1.0+0.0000000000000000004#i
2.0
-1.0-0.0000000000000000006#i
-1.0+0.0000000000000000008#i
2.0
17.9999999999999999997-0.0000000000000000005#i

Regardless of whether x = -1/2 - i*sqrt(3)/2 or -1/2 + i*sqrt(3)/2, the terms being added are in sequence (-1)^2, (-1)^2, 2^2, repeated three times, or 1+1+4+1+1+4+1+1+4 = 18.

 Posted by Charlie on 2015-01-14 10:47:33

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