If x²-5x+1=0, find the value of (x^10+1)/x^5
options:
a) 2524 b)2525 c)2424 d)2010
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Answered by
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ANSWER IS b) 2525
=> x^2 + 1 = 5x divide by x
x +1/x = 5 ---- 1 (square on both sides
x ^2 + 1/x^2 =23 -----2
multiply both equations which gives
x^3 +1/x^3 +(1/x + x) =115
x^3 + 1/x^3 = 110 ------3
square on both sides 2nd equation
x^4 + 1/x^4 = 527 multiply this equation
with 1st equation
x^5 + 1/x^5 + x^3 +1/x^3 = 2635 substitute
3rd equation
x^5 + 1/x^5 = 2525 ans
i hope its hlp you
=> x^2 + 1 = 5x divide by x
x +1/x = 5 ---- 1 (square on both sides
x ^2 + 1/x^2 =23 -----2
multiply both equations which gives
x^3 +1/x^3 +(1/x + x) =115
x^3 + 1/x^3 = 110 ------3
square on both sides 2nd equation
x^4 + 1/x^4 = 527 multiply this equation
with 1st equation
x^5 + 1/x^5 + x^3 +1/x^3 = 2635 substitute
3rd equation
x^5 + 1/x^5 = 2525 ans
i hope its hlp you
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Answer:
answer is 2525
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