[tex]x+\dfrac{1}{x}=3 \Leftrightarrow (x+\dfrac{1}{x})^2 = 3^2 \Leftrightarrow x^2+2\cdot \not{x}\cdot\dfrac{1}{\not{x}}+\dfrac{1}{x^2} =9 \Leftrightarrow
\\\;\\
\Leftrightarrow x^2+2+\dfrac{1}{x^2} = 9 \Leftrightarrow x^2+\dfrac{1}{x^2} =9-2\Leftrightarrow x^2+\dfrac{1}{x^2} =7.[/tex]
