Question

If x - 1/x = 2√3, then find the value of x⁵ + 1/x⁵.
1. 750
2. 724
3. 841
4. 784

Answer 1

Correct Answer - Option 2 : 724

Given:

x - 1/x = 2√3

Formula used:

If x - 1/x = t, then x + 1/x = √(t² + 4)

If x + 1/x = p, then x5 + 1/x5 = {(p² - 2) × (p³ - 3p)} - p

Calculations:

x - 1/x = 2√3

⇒ x + 1/x = √{(2√3)² + 4}

⇒ 4

x5 + 1/x5 = {(4² - 2) × (4³ - 3 × 4)} - 4

⇒ 14 × 52 - 4

⇒ 724

∴ The value of  x5 + 1/x5  is 724.