If x + 1/x = 1 , then the value of x^2 + 3x + 1x^2 + 7x + 1 is?

Answer: Option A

$$\begin{array}{rl}& \text{Given, }x+\frac{1}{x}=1\\ & \text{Find }\frac{x^2+3x+1}{x^2+7x+1}\\ & \text{From equation (i)}\\ & \Rightarrow x+\frac{1}{x}=1\\ & \Rightarrow x^2+1=x\\ & \Rightarrow \frac{\left(x^2+1\right)+3x}{\left(x^2+1\right)+7x}\\ & \Rightarrow \frac{x+3x}{x+7x}\\ & \Rightarrow \frac{4x}{8x}\\ & \Rightarrow \frac{1}{2}\end{array}$$