If x+\(\frac{1}{x}\) = 3, then x⁵+\(\frac{1}{{x}^{5}}\) equals to:

123

x+\(\frac{1}{x}\) = 3,

x²+\(\frac{1}{{x}^{2}}\) = 7 and

x³+\(\frac{1}{{x}^{3}}\) = 18

Now,

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

                                         = (7) (18) - 3 = 126 - 3 = 123