SSC CGL 2023 PYQ — Question 54

The correct answer is option 3 i.e. 396√6.

Given that

If $(x-\frac{1}{x})=2\sqrt{2}$ and x > 1

Cubing both sides

⇒ x³ - 1/x³ - 3 (x - 1/x) = 16√2

⇒ x³ - 1/x³ = 16√2 + 6√2 = 22√2

As we know,

⇒ (x + 1/x)² = (x - 1/x)² + 4 = 8 + 4 =12

⇒ x + 1/x = 2√3

Cubing both sides

⇒ x³ + 1/x³ + 3 (x + 1/x) = 24√3

⇒ x³ + 1/x³ = 24√3 - 6√3 = 18√3

Hence, $(x^6-\frac{1}{x^6})$ = (x³ + 1/x³)(x³ - 1/x³ ) = 22√2 × 18√3 = 396√6