If x + 14x = 3/2 , find the value of 8x^3 + 18x^3 = ?

Answer: Option A

$$\begin{array}{rl}& x+\frac{1}{4x}=\frac{3}{2}\\ & \text{Multiply by 2 both sides}\\ & \therefore 2x+\frac{1}{2x}=3\\ & \text{Take cube both sides}\\ & \Rightarrow {\left(2x+\frac{1}{2x}\right)}^3={\left(3\right)}^3\\ & \Rightarrow \text{8}{x}^3\text{ + }\frac{1}{8x^3}+3.2x.\frac{1}{2x}\left(2x\text{ + }\frac{1}{2x}\right)=27\\ & \Rightarrow \text{8}{x}^3\text{ + }\frac{1}{8x^3}+3\left(3\right)=27\\ & \Rightarrow \text{8}{x}^3\text{ + }\frac{1}{8x^3}=18\end{array}$$