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

Answer: Option B

$$\begin{array}{rl}& x\left(3-\frac{2}{x}\right)=\frac{3}{x}\\ & \Rightarrow 3x-2=\frac{3}{x}\\ & \Rightarrow 3x-\frac{3}{x}=2\\ & \Rightarrow 3\left(x-\frac{1}{x}\right)=2\\ & \Rightarrow x-\frac{1}{x}=\frac{2}{3}\\ & \left(\text{Squaring both sides}\right)\\ & \Rightarrow x^2\text{ + }\frac{1}{x^2}-2=\frac{4}{9}\\ & \Rightarrow x^2\text{ + }\frac{1}{x^2}=\frac{4}{9}+2\\ & \Rightarrow x^2\text{ + }\frac{1}{x^2}=2\frac{4}{9}\end{array}$$