If x - 1/x = 2 √15 then find the value of x3 + 1/(x^3)

⇒ 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 - \(\frac{1}{x}\) = 2\(\sqrt{15}\), then 

⇒ x + \(\frac{1}{x}\) = \(\sqrt {(2\sqrt{15})^2 + 4}\) = 8

⇒ x³ + \(\frac{1}{x^3}\) = 8³ - 3 × 8 = 488