Question

If x² - 6√3x + 1 = 0 then find the value of x³ + 1/x³. 
1. 648√3
2. 615√2
3. 630√3
4. 620√3

Answer 1

Correct Answer - Option 3 : 630√3

Given:

x2 - 6√3x + 1 = 0

Formula used:

(x + y)³ = x³ + y³ + 3xy(x + y)

Calculation:

x2 - 6√3x + 1 = 0

Divide the above equation by x

⇒ x + 1/x = 6√3

cubing on both side

⇒ (x + 1/x)³ = (6√3)³

⇒ x³ + 1/x³  + 3 × x × 1/x(x + 1/x) = 648√3

⇒ x3 + 1/x³ + 3 × 6√3 = 648√3

⇒ x3 + 1/x3 + 18√3 = 648√3

⇒ x3 + 1/x³ =  648√3 - 18√3

⇒ x3 + 1/x3 = 630√3

∴ the value of x3 + 1/x³ is 630√3