Question:
If x2 - 8x = 1, then find the value of {(x6 + 12x3 - 1)/(x6 - 24x3- 1)}
If x2 - 8x = 1, then find the value of {(x6 + 12x3 - 1)/(x6 - 24x3- 1)}
Updated On: Sep 10, 2024
- \(\frac{133}{118}\)
- \(\frac{141}{135}\)
- \(\frac{121}{115}\)
- \(\frac{137}{128}\)
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The Correct Option is D
Solution and Explanation
Since, x2 - 8x - 1 = 0
So, x - 1/x = 8
Or, x3 - 1/x3 = (x - 1/x)3 + 3(x - 1/x)
Or, x3 - 1/x3 = 83 + 3 × 8
Or, x3 - 1/x3 = 512 + 24 = 536
So, {(x6 + 12x3 - 1)/(x6 - 18x3 - 1)}
On dividing numerator and denominator by x3
= {(x3 - 1/x3) + 12}/{(x3 - 1/x3) – 24} = {(536 + 12)/(536 - 24)}
Or, {(x3 - 1/x3) + 12}/{(x3 - 1/x3) – 24} = 548/512 = 137/128
So, the correct option is (D) : \(\frac{137}{128}\)
So, x - 1/x = 8
Or, x3 - 1/x3 = (x - 1/x)3 + 3(x - 1/x)
Or, x3 - 1/x3 = 83 + 3 × 8
Or, x3 - 1/x3 = 512 + 24 = 536
So, {(x6 + 12x3 - 1)/(x6 - 18x3 - 1)}
On dividing numerator and denominator by x3
= {(x3 - 1/x3) + 12}/{(x3 - 1/x3) – 24} = {(536 + 12)/(536 - 24)}
Or, {(x3 - 1/x3) + 12}/{(x3 - 1/x3) – 24} = 548/512 = 137/128
So, the correct option is (D) : \(\frac{137}{128}\)
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