If 2x + 14x = 1 , then the value of x^2 + 164x^2 is?

Answer: Option A

$$\begin{array}{rl}& 2x+\frac{1}{4x}=1\\ & \text{Dividing by 2 both side}\\ & \Rightarrow x+\frac{1}{8x}=\frac{1}{2}\\ & \text{Squaring both side }\\ & \Rightarrow x^2+\frac{1}{64x^2}+2\times x\times \frac{1}{8x}=\frac{1}{4}\\ & \Rightarrow x^2+\frac{1}{64x^2}+\frac{1}{4}=\frac{1}{4}\\ & \Rightarrow x^2+\frac{1}{64x^2}=\frac{1}{4}-\frac{1}{4}\\ & \Rightarrow x^2+\frac{1}{64x^2}=0\end{array}$$