If x - \(\frac{1}{x}\) = 2\(\sqrt{15}\)

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

512

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

Here,

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

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

⇒ ( x + \(\frac{1}{x}\) )³ = 8³ = 512