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

Given 2x+$$\frac{1}{x} =$$ 3

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

$$\Rightarrow$$ x+$$\frac{1}{x} = \frac{3}{2}$$

Cubing on both sides

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

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

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

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

$$x^{3}+\frac{1}{x^{3}}+2 = \frac{-9}{8}+2 = \frac{7}{8}$$