If x2 - 3x + 1 = 0, then the value of x^2 + x + 1/x + 1x^2 is?

Answer: Option A

$$\begin{array}{rl}& x^2-3x+1=0\\ & \Rightarrow x^2+1=3x\\ & \Rightarrow x+\frac{1}{x}=3\\ & \text{Squaring both sides}\\ & \Rightarrow x^2+\frac{1}{x^2}+2=9\\ & \Rightarrow x^2+\frac{1}{x^2}=7\\ & \therefore x^2+x+\frac{1}{x}+\frac{1}{x^2}\\ & \Rightarrow x^2+\frac{1}{x^2}+x+\frac{1}{x}\\ & \Rightarrow 7+3\\ & \Rightarrow 10\end{array}$$