If x - 3/x = 6, x ≠ 0, then the value of (x⁴ - 27/(x²))/(x²-3x-3) is:

If x - 3/x = 6, x ≠ 0, then the value of (x⁴…

If x - 3/x = 6, x ≠ 0, then the value of $\frac{x^4 - \frac{27}{x^2}}{x^2-3x-3}$ is:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 90

x - 3/x = 6..........(1)

On cubing both sides we get,

x³ - 27/x³ - 3 × x × 3/x(x - 3/x) = 216

x³ - 27/x³ - 54 = 216

x³ - 27/x³ = 270..............(2)

$\frac{x^4 - \frac{27}{x^2}}{x^2-3x-3}$ ,

On dividing the numerator and denominator by x we get,

= (x³ - 27/x³)/(x - 3/x - 3)

= 270/(6 - 3)

= 270/3 = 90.