x2 + \(\frac{1}{x^2}\) = 7  (x > 0), then find the value of x5 + \(\frac{1}{x^5}\).

121 122 145 123

123

x2 + \(\frac{1}{x^2}\) = 7 (x + \(\frac{1}{x}\)) = \(\sqrt {7\;+\;2}\) =3 x3 + \(\frac{1}{x^3}\) = 27 - 3(3) = 18 Now, x5 + \(\frac{1}{x^5}\) = (x2 + \(\frac{1}{x^2}\)) (x3 + \(\frac{1}{x^3}\)) - (x + \(\frac{1}{x}\)) = (7 × 18) -3  =  123