If $$2x-\frac{2}{x}=1(x\neq0)$$, then the value of $$x^3-\frac{1}{x^3}$$ is

Expression : $$2x-\frac{2}{x}=1$$

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

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

Cubing both sides, we get :

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

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

Substituting value from equation (i)

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

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

=> $$x^3-\frac{1}{x^3}=\frac{1+12}{8}=\frac{13}{8}$$

=> Ans - (B)