[tex]\displaystyle\\
\frac{1}{a}-a =8~~\Big|~\text{(Ridicam la patrat)}\\\\
\left(\frac{1}{a}-a\right)^2=8^2\\\\
\frac{1}{a^2}-2\times\frac{1}{a}\times a+a^2=8^2\\\\
\frac{1}{a^2}-2\times\frac{a}{a}+a^2=64\\\\
\frac{1}{a^2}-2 +a^2=64\\\\
\frac{1}{a^2}+a^2=64+2\\\\
\boxed{a^2+\frac{1}{a^2}=66}~\text{Rezultat intermediar.}\\\\\\
a^2+\frac{1}{a^2}=66~\Big|~\text{(Ridicam la patrat)}\\\\
\left(a^2+\frac{1}{a^2}\right)^2=66^2\\\\
a^4 +2\times a^2\times\frac{1}{a^2}+\frac{1}{a^4}=4356
[/tex]
[tex]\displaystyle\\
a^4 +2\times \frac{a^2}{a^2}+\frac{1}{a^4}=4356\\\\
a^4 +2+\frac{1}{a^4}=4356\\\\
a^4 +\frac{1}{a^4}=4356-2\\\\
\boxed{\boxed{a^4 +\frac{1}{a^4}=4354}}~~~\text{Rezultat final} [/tex]
