Question

Dado que a + a^-1=3, obtenha o valor numérico de a^2 + a^-2.

Answer 1

Bruna,
Vamos passo a passo

              $a+a^{-1} =3 \\ \\ a+ \frac{1}{a} =3 \\ \\ (a + \frac{1}{a} )^2=3^2 \\ \\ a^2+2.a. \frac{1}{a} + \frac{1}{a^2} =9 \\ \\ a^2+ \frac{1}{a^2} =9-2$

               $a^2+ a^{-2} =7$  RESULTADO FINAL

Answer 2

$a+ \frac{1}{a} =3\\ \\\left(a+ \frac{1}{a} \right)^2=3^2\\ \\a^2+2\cdot a\cdot\frac{1}{a} +(\frac{1}{a})^2=9\\ \\a^2+2 +(\frac{1}{a})^2=9\\ \\ a^2+\frac{1}{a^2}=9-2\\ \\a^2+\frac{1}{a^2}=7\\ \\ Obs.: a \neq 0$