If x + 1/x = 2 and x is real, then the value of x^17 + 1x^19\, is?

Answer: Option C

$$\begin{array}{rl}& x+\frac{1}{x}=2\\ & \left(\text{Assume }x=1\text{, so, }1+1=2\right)\\ & x^{17}\text{ + }\frac{1}{x^{19}}\\ & ={\left(1\right)}^{17}+\frac{1}{{\left(1\right)}^{19}}\\ & =1+1\\ & =2\end{array}$$