If $$ x + \frac{1}{x} = 3$$, the value of $$x^5 + \frac{1}{x^5}$$ is

given that $$ x + \frac{1}{x} = 3$$, and we need to find the value of $$x^5 + \frac{1}{x^5}$$

 $$(x + \frac{1}{x})^{2} = 3^{2}$$ = $$ x^{2} + \frac{1}{x}^{2} = 9 - 2 = 7 $$

 $$( x + \frac{1}{x} )^{3} = 3^{3}$$ = $$ x^{3} + \frac{1}{x}^{3} + 3(x + \frac{1}{x})$$ = 27 

 $$ x^{3} + \frac{1}{x}^{3}$$ = 27 - 9 = 18 

$$x^5 + \frac{1}{x^5}$$ = $$ (x^{2} + \frac{1}{x}^{2})(x^{3} + \frac{1}{x}^{3}) - (x +\frac{1}{x})$$

$$x^5 + \frac{1}{x^5}$$ = 123