12.
[tex]\it a^4+\dfrac{1}{a^4}=\dfrac{6817}{1296}\Big|_{-2} \Rightarrow a^4-2+\dfrac{1}{a^4}=\dfrac{4225}{1296} \Rightarrow \Big(a^2-\dfrac{1}{a^2}\Big)^2=\dfrac{65^2}{36^2} \Rightarrow \\ \\ \\ \Rightarrow a^2-\dfrac{1}{a^2}=\dfrac{65}{36}\Big|_{-2} \Rightarrow (a-\dfrac{1}{a})^2=\dfrac{25}{36} \Rightarrow a-\dfrac{1}{a}=\dfrac{5}{6}[/tex]
