If x^2 - 3x + 1 = 0, then the value of x^3 + 1x^3\, is?

Answer: Option B

$$\begin{array}{rl}& x^2-3x+1=0\\ & x^2+1=3x\\ & \text{Divide by }x\\ & \frac{x^2}{x}+\frac{1}{x}=\frac{3x}{x}\\ & \Rightarrow x+\frac{1}{x}=3\\ & \text{Cubing both sides}\\ & \Rightarrow x^3\text{ + }\frac{1}{x^3}+3x\times \frac{1}{x}\left(x+\frac{1}{x}\right)=27\\ & \Rightarrow x^3\text{ + }\frac{1}{x^3}+3\times 3=27\\ & \Rightarrow x^3\text{ + }\frac{1}{x^3}=18\end{array}$$