SSC CGL 2022 PYQ — Question 74

The correct answer is option 3 i.e.724.

Given:

x + 1/x = 4

Formula used:

If x + 1/x = k

Then on squaring both sides we get

x² + 1/x² = k² - 2.

On cubing both sides we get

x³ + 1/x³ = k³ - 3k

And, x⁵ + 1/x⁵ = (x² + 1/x²) × (x³ + 1/x³) - (x + 1/x)

Calculation:

x + 1/x = 4 ----(1)

Square both sides of equation (1)

= x² + 1/x² = 4² - 2

= x² + 1/x² = 14

Cubing both sides of equation (1)

⇒ x³ + 1/x³ = 4³ - 3 × 4

⇒ x³ + 1/x³ = 64 - 12

⇒ x³ + 1/x³ = 64 - 12

⇒ x³ + 1/x³ = 52

Now apply the formula of x⁵ + 1/x⁵

⇒ 14 × 52 - 4

⇒ 728 - 4 = 724

The value of x⁵ + 1/x⁵ is 724.