[tex]x-\dfrac{1}{x}=3 \Rightarrow \left(x-\dfrac{1}{x}\right)^2=3^2 \Rightarrow x^2-2\cdot x\cdot\dfrac{1}{x} +\left(\dfrac{1}{x}\right)^2 =9
\\\;\\
\Rightarrow x^2-2+\dfrac{1}{x^2}=9 \ \Rightarrow \ x^2+\dfrac{1}{x^2} =9+2 \ \Rightarrow \ x^2+\dfrac{1}{x^2} = 11
\\
.[/tex]
