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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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Solution computer solution | Comment 1 of 4
x = (5 +/- sqrt(25-8)) / 4
  = 5/4 +/- sqrt(17)/4
  
a = (5 + sqrt(17))/4  
b = (5 - sqrt(17))/4 

    5   point 120
   10   A=(5+sqrt(17))/4
   20   B=(5-sqrt(17))/4
   30   print (4*fnS(2017)+fnS(2015))/fnS(2016)
  100   end
  200   fnS(X)
  210    S=A^(2*X)+B^(2*X)
  220   return(S)

results in 21.0.

(Point 120 calls for 577 decimal positions after the decimal point.)

In fact, (4*S(k+1)+S(k-1))/S(k) = 21 for any k, even zero or negative.

  Posted by Charlie on 2016-10-21 14:46:29
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