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A little twist (Posted on 2016-10-21) Difficulty: 3 of 5
If a, b are the roots of 2x^2 - 5x + 1 = 0 and

S(n) = a^(2n) + b^(2n)

then find the value of (4*S(2017) + S(2015)) / S(2016)

No Solution Yet Submitted by Danish Ahmed Khan    
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re(2): computer solution.....yes,but... | Comment 3 of 4 |
(In reply to re: computer solution.....yes,but... by Ady TZIDON)

The text does define S(x) for non-positive x, and the evaluation is not recursive, but direct.

for x = -2, x+1 = -1, x-1 = -3

S(-3) =  ((5 + sqrt(17))/4)^-6 + ((5 - sqrt(17))/4)^-6 
       ~= 0.00710401270584942 + 9008.99289598726
       ~= 9009 (actually exactly equal S(-3)

Similarly

S(-2) =  ((5 + sqrt(17))/4)^-4 + ((5 - sqrt(17))/4)^-4
         = 433

S(-1) =  ((5 + sqrt(17))/4)^-2 + ((5 - sqrt(17))/4)^-2
         = 21

(4*21 + 9009) / 433 = 21

  Posted by Charlie on 2016-10-22 08:50:05
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