If x - \(\frac{1}{x}\) = 4\(\sqrt{2}\)

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

198

⇒ 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 - \(\frac{1}{x}\) = 4\(\sqrt{2}\), then 

⇒ x + \(\frac{1}{x}\) = \(\sqrt {(4\sqrt{2})^2 + 4}\) = 6

⇒ x³ + \(\frac{1}{x^3}\) = 6³ - 3 × 6 = 198