Question

Se 2^x + 2^-x =3 então 4^x+4^-x é

Answer 1

2^x + 2^-x =3
(2^x + 2^-x)²  = 3²

obs : (2^x)² = 2^2x = (2²)^x = 4^x

4^x + 4^-x + 2.2^x.2^-x = 9
4^x + 4^-x + 2.1 = 9
4^x + 4^-x = 7 (resp)

Answer 2

Olá, Audianne.

$2^x + 2^{-x} =3\Rightarrow \\\\(2^x + 2^{-x})\² = 3\²\Rightarrow \\\\ (2^x)\² +2\cdot2^x\cdot2^{-x}+(2^{-x})^2= 9\Rightarrow \\\\ (2^2)^x +2\cdot2^0+(2^2)^{-x}= 9\Rightarrow$

$4^x + 2 + 4^{-x} = 9\Rightarrow\\\\ 4^x + 4^{-x} = 9-2\Rightarrow\\\\ \boxed{4^x + 4^{-x} = 7}$