If x + 1/x = 3 , then the value of ( x^5 + 1x^5 )\, is?

Answer: Option C

$$\begin{array}{rl}& x+\frac{1}{x}=3\\ & \left(\text{Squaring both sides}\right)\\ & x^2+\frac{1}{x^2}=7\\ & \text{On cubing both sides}\\ & x^3+\frac{1}{x^3}+3.x.\frac{1}{x}\left(x+\frac{1}{x}\right)=27\\ & \Rightarrow x^3+\frac{1}{x^3}+3\times 3=27\\ & \Rightarrow x^3+\frac{1}{x^3}=18\\ & \therefore \left(x^3+\frac{1}{x^3}\right)\left(x^2+\frac{1}{x^2}\right)=18\times 7\\ & \Rightarrow \left(x^5+\frac{1}{x^5}\right)+\left(x+\frac{1}{x}\right)=126\\ & \Rightarrow \left(x^5+\frac{1}{x^5}\right)+3=126\\ & \Rightarrow \left(x^5+\frac{1}{x^5}\right)=123\end{array}$$