If 2x + 12x = 2, then what is the value of 2 ( 1/x )^4 + ( 1/x )^5 ?

Answer: Option D

$$\begin{array}{rl}& 2x+\frac{1}{2x}=2\\ & \text{Now, }2x=1\\ & \Rightarrow x=\frac{1}{2}\\ & \Rightarrow \frac{1}{x}=2\\ & \sqrt{2{\left(\frac{1}{x}\right)}^4+{\left(\frac{1}{x}\right)}^5}\\ & =\sqrt{2\times 2^4+2^5}\\ & =\sqrt{32+32}\\ & =\sqrt{64}\\ & =8\end{array}$$