If $$2x+\frac{2}{x}=3$$ than the value of $$x^{3}+\frac{1}{x^{3}}+2$$ is

Expression : $$2x+\frac{2}{x}=3$$

=> $$2(x+\frac{1}{x})=3$$

=> $$x+\frac{1}{x}=\frac{3}{2}$$ ---------(i)

Cubing both sides, we get :

=> $$(x+\frac{1}{x})^3=(\frac{3}{2})^3$$

=> $$x^3+\frac{1}{x^3}+3.x.\frac{1}{x}(x+\frac{1}{x})=\frac{27}{8}$$

Substituting value from equation (i)

=> $$x^3+\frac{1}{x^3} + 3(\frac{3}{2})=\frac{27}{8}$$

=> $$x^3+\frac{1}{x^3}=\frac{27}{8}-\frac{9}{2}$$

=> $$x^3+\frac{1}{x^3}=\frac{27-36}{8}=\frac{-9}{8}$$

Adding 2 on both sides, we get :

=> $$x^3+\frac{1}{x^3}+2=2-\frac{9}{8}$$

=> $$x^3+\frac{1}{x^3}+2=\frac{7}{8}$$

=> Ans - (D)