Correct Answer: $\frac{7}{8}$

Solution : Given: $2x+\frac{2}{x}=3$
⇒ $x+\frac{1}{x}=\frac{3}{2}$ (Dividing both sides by 2)
Now, $(x+\frac{1}{x})^3=(\frac{3}{2})^3$ (Taking cube on both sides)
⇒ $x^3+\frac{1}{x^3}+3×x×\frac{1}{x}(x+\frac{1}{x})=\frac{27}{8}$
⇒ $x^3+\frac{1}{x^3}+3(\frac{3}{2})=\frac{27}{8}$
⇒ $x^3+\frac{1}{x^3}=\frac{27}{8}–\frac{9}{2}$
⇒ $x^3+\frac{1}{x^3}+2=\frac{27}{8}–\frac{9}{2}+2=\frac{27–36+16}{8}=\frac{7}{8}$
Hence, the correct answer is = $\frac{7}{8}$.