If x + \(\frac{1}{x}\) = 4

Find x⁵ + \(\frac{1}{x^5}\)

724

Formula → [x⁵ + \(\frac{1}{x^5}\) = (x³ + \(\frac{1}{x^3}\)) (x² + \(\frac{1}{x^2}\)) - (x + \(\frac{1}{x}\))]

            → [x² + \(\frac{1}{x^2}\) = a² - 2 If x + \(\frac{1}{x}\) = a]

            → [x³ + \(\frac{1}{x^3}\) = a³ - 3a]

x + \(\frac{1}{x}\) = 4

x² + \(\frac{1}{x^2}\) = 4² - 2 = 14

x³ + \(\frac{1}{x^3}\) = (4)³ - 3 × 4 = 52

Now; x⁵ + \(\frac{1}{x^5}\) = 52 × 14 - 4 = 724