Question

QUESTÃO 33.
segue em anexo 
eu sei que dar 98 mas quero o calculo

Answer 1

Essa é fácil:

Vamos começar por:

$3^n+3^{-n}=10\\ \\ (3^n+3^{-n})^2=10^2\\ \\ (3^n)^2+(3^{-n})^2+2.3^n.3^{-n}=100\\ \\ (3^2)^n+3^2)^{-n}+2=100\\ \\ 9^n+9^{-n}=100-2\\ \\ \boxed{9^n+9^{-n}=98}$

Answer 2

 Olá Bruno,
boa noite!

$9^n+9^{-n}=\\\\(3^2)^n+(3^2)^{-n}=\\\\3^{2n}+3^{-2n}=\\\\3^{2n}+\frac{1}{3^{2n}}=\\\\(3^n+\frac{1}{3^n})^2-2\cdot3^n\cdot\frac{1}{3^n}=\\\\(10)^2-\frac{2\cdot3^n}{3^n}=\\\\100-2=\\\\\boxed{98}$