Correct Answer - Option 3 : 630√3

**Given:**

x2 - 6√3x + 1 = 0

**Formula used:**

(x + y)^{3} = x^{3} + y^{3} + 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}

⇒ x^{3} + 1/x^{3 }+ 3 × x × 1/x(x + 1/x) = 648√3

⇒ x3 + 1/x^{3} + 3 × 6√3 = 648√3

⇒ x3 + 1/x3 + 18√3 = 648√3

⇒ x3 + 1/x^{3} = 648√3 - 18√3

⇒ x3 + 1/x3 = 630√3

**∴ the value of x3 + 1/x**^{3} is 630√3