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