Question

Olá. Alguém poderia me ajudar a resolver isso?

 

Se 3^x + 3^(-x) = 7, então 3^3x + 3^(-3x) vale? 

(Resposta:322)

Answer 1

 Olá,

$\left(3^{x}+3^{-x}\right)^3=(7)^3\\\\3^{3x}+3\cdot3^{2x}\cdot3^{-x}+3\cdot3^x\cdot3^{-2x}+3^{-3x}=343\\\\3^{3x}+3\cdot3^x+3\cdot3^{-x}+3^{-3x}=343\\\\3^{3x}+3\underbrace{(3^x+3^{-x})}_{7}+3^{-3x}=343\\\\3^{3x}+3^{-3x}=343-21\\\\\boxed{3^{3x}+3^{-3x}=322}$