SSC CGL 2023 PYQ — Question 72

The correct answer is option 2 i.e. 992√15

Given that

If ( x - $\frac{1}{x}$ ) = √6, and x > 1,

Square both sides

⇒ ( x - $\frac{1}{x}$ )² = 6

⇒ x² + 1/x² - 2 = 6

⇒ x² + 1/x² = 8 

Again, square both sides

⇒ (x² + 1/x² )² = 8²

⇒ x⁴ + 1/x⁴ + 2 = 64

⇒ x⁴ + 1/x⁴ = 62

And We can write 

x + 1/x = √[( x - $\frac{1}{x}$ )² + 4] =  √(6 + 4 ) =  √10

Hence, the value  of ( x⁸ - $\frac{1}{x^8})$

= (x⁴ + 1/x⁴) (x² + 1/x²) (x + 1/x) ( x - $\frac{1}{x}$) 

= 62 × 8 × √10 × √6 = 992√15