If x 2 - 8x = 1, then find the value of {(x 6 + 12x 3 - 1)/(x 6 - 24x 3 - 1)}

Since, x 2 - 8x - 1 = 0 So, x - 1/x = 8 Or, x 3 - 1/x 3 = (x - 1/x) 3 + 3(x - 1/x) Or, x 3 - 1/x 3 = 8 3 + 3 × 8 Or, x 3 - 1/x 3 = 512 + 24 = 536 So, {(x 6 + 12x 3 - 1)/(x 6 - 18x 3 - 1)} On dividing numerator and denominator by x 3 = {(x 3 - 1/x 3 ) + 12}/{(x 3 - 1/x 3 ) – 24} = {(536 + 12)/(536 - 24)} Or, {(x 3 - 1/x 3 ) + 12}/{(x 3 - 1/x 3 ) – 24} = 548/512 = 137/128 So, the correct option is (D) : $\frac{137}{128}$

Question:

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}

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If x2 - 8x = 1, then find the value of {(x6 + 12x3 - 1)/(x6 - 24x3- 1)}

The Correct Option is D

Solution and Explanation

Top Questions on Number Systems

Questions Asked in CAT exam

If x² - 8x = 1, then find the value of {(x⁶ + 12x³ - 1)/(x⁶ - 24x³- 1)}