If (x² + 1/(x²)) = 18 and x > 1, what is the value of (x³ - 1/(x³)) ?

SSC Selection Post 2023 PYQ — Question 64

If $(x^2 + \frac{1}{x^2}) = 18$ and x > 1, what is the value of $(x^3 - \frac{1}{x^3}) ?$

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 76.

x² + 1/x² = 18

⇒ x + 1/x = √(18 - 2) = 4

⇒ x³ - 1/x³ = 4³ + 3 × 4 = 64 + 12 = 76