x² + \(\frac{1}{x^2}\) = 98  (x > 0), then find the value of x⁵ + \(\frac{1}{x^5}\).

95050

x² + \(\frac{1}{x^2}\) = 98 

(x + \(\frac{1}{x}\)) = \(\sqrt {98\;+\;2}\) = 10

x³ + \(\frac{1}{x^3}\) = 1000 - 3(10) = 970

Now, x⁵ + \(\frac{1}{x^5}\) = (x² + \(\frac{1}{x^2}\)) (x³ + \(\frac{1}{x^3}\)) - (x + \(\frac{1}{x}\))

= (98 × 970) - 10 = (100 × 970) - (2 × 970) - 10 = 97000 - 1940 - 10 = 97000 - 1950 = 95050