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

Answer: Option C

$$\begin{array}{rl}& 2x+\frac{2}{x}=3\\ & \Rightarrow x+\frac{1}{x}=\frac{3}{2}\\ & \text{Taking cube on both sides}\\ & \Rightarrow {\left(x+\frac{1}{x}\right)}^3={\left(\frac{3}{2}\right)}^3\\ & x+\frac{1}{x}=a\\ & x^3+\frac{1}{x^3}=a^3-3a\\ & \Rightarrow x^3+\frac{1}{x^3}+3\left(x+\frac{1}{x}\right)=\frac{27}{8}\\ & \Rightarrow x^3+\frac{1}{x^3}+3\times \frac{3}{2}=\frac{27}{8}\\ & \Rightarrow x^3+\frac{1}{x^3}=\frac{27}{8}-\frac{9}{2}\\ & \Rightarrow x^3+\frac{1}{x^3}=\frac{-9}{8}\\ & \therefore x^3+\frac{1}{x^3}+2\\ & =\frac{-9}{8}+2\\ & =\frac{-9+16}{8}\\ & =\frac{7}{8}\end{array}$$