If x - \(\frac{1}{x}\) = 8\(\sqrt{3}\)

then find the value of  x³ + \(\frac{1}{x^3}\)

2702

⇒ If x - \(\frac{1}{x}\) = a then x + \(\frac{1}{x}\) = \(\sqrt {a^2 + 4}\)

and

If x + \(\frac{1}{x}\) = a then ⇒ x³ + \(\frac{1}{x^3}\) = a³ - 3a

ATQ,

x - \(\frac{1}{x}\) = 8\(\sqrt{3}\), then 

⇒ x + \(\frac{1}{x}\) = \(\sqrt {(8\sqrt{3})^2 + 4}\) = 14

⇒ x³ + \(\frac{1}{x^3}\) = 14³ - 3 × 14 = 2702