SSC CGL 2023 PYQ — Question 72

The correct answer is option 1 i.e. $140\sqrt{2}$.

$\left ( x+\frac{1}{x} \right )=2\sqrt{2}$

Cubing both sides

⇒ x³ + 1/x³ + 3 (x + 1/x) = 16√2

⇒ x³ + 1/x³ = 16√2 - 6√2 = 10√2

As we know,

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

⇒ (x - 1/x) = 2

Cubing both sides

⇒ x³ - 1/x³ - 3 (x - 1/x) = 8

⇒ x³ - 1/x³ = 8 + 6 = 14

Hence, $\left ( x^6-\frac{1}{x^6} \right )$ = (x³ + 1/x³ )(x³ - 1/x³) = 10√2 × 14 = 140√2