[tex] a+\dfrac{1}{a} = 3\Big|^2 \Rightarrow \Big(a+\dfrac{1}{a} \Big)^2 = 3^2 \Rightarrow \\ \\ \Rightarrow a^2+2\cdot a\cdot \dfrac{1}{a} + \Big(\dfrac{1}{a} \Big)^2 = 9 \Rightarrow a^2 + 2+ \dfrac{1}{a^2} = 9 \Rightarrow \\ \\ \Rightarrow a^2+ \dfrac{1}{a^2} = 9-2 \Rightarrow \boxed{\boxed{a^2+ \dfrac{1}{a^2} = 7 }}[/tex]
