If x - \(\frac{1}{x}\) = 3\(\sqrt{5}\)

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

322

⇒ 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 - \(\frac{1}{x}\) = 3\(\sqrt{5}\), then 

⇒ x + \(\frac{1}{x}\) = \(\sqrt {(3\sqrt{5})^2 + 4}\) = 7

⇒ ( x³ + \(\frac{1}{x^3}\) ) = 7³ - 3 × 7 = 322