If 2x + 29x = 4 , then the value of 27x^3 + 127x^3 is?

Answer: Option B

$$\begin{array}{rl}& 2x+\frac{2}{9x}=4\\ & \text{Multiply by }\frac{3}{2}\text{ on both sides}\\ & \Rightarrow 3x+\frac{1}{3x}=6\\ & \text{Taking cube on both sides}\\ & \Rightarrow {\left(3x+\frac{1}{3x}\right)}^3=6^3\\ & \Rightarrow 27x^3+\frac{1}{27x^3}+3\times 3x\times \frac{1}{3x}\left(3x+\frac{1}{3x}\right)=216\\ & \Rightarrow 27x^3+\frac{1}{27x^3}+3\times 6=216\\ & \Rightarrow 27x^3+\frac{1}{27x^3}=216-18\\ & \Rightarrow 27x^3+\frac{1}{27x^3}=198\end{array}$$