Pentru a rezolva exercitiul ne vom folosi de un artificiu si vom ridica relatia la patrat.
[tex](a+\frac{1}{a}) ^{2}=3^{2}\\\\a^{2}+2a\frac{1}{a}+\frac{1}{a^{2}}=9\\\\a^{2}+2+\frac{1}{a^{2}}=9\\\\\\a^{2}+\frac{1}{a^{2}}=9-2\\\\a^{2}+\frac{1}{a^{2}}=7[/tex]
