SSC CGL 2023 PYQ — Question 61

The correct answer is option 3 i.e. - 8886.

Given that

If x - $\frac{1}{x}$= - 6

Squaring both sides

⇒ x² + 1/x² - 2 = 36

⇒ x² + 1/x² = 38 

Now,  x - $\frac{1}{x}$= - 6

Cube both sides

⇒ x³ - 1/x³ - 3(x - 1/x) = - 216

⇒ x³ - 1/x³ = -216 - 18 = - 234

As we know,

⇒ x⁵ - $\frac{1}{x^5}$ = (x³ - 1/x³) (x² + 1/x²) - ( x - $\frac{1}{x}$ )

= - 234 × 38 - (- 6) = - 8892 + 6 = - 8886