Question

Exponencial pf , me ajudaaa ,se $2^x+2 ^{-x} =3 \\ entao \\ 8^x+8 ^{-x}$  
é?

Obs.: a resposta é 18

Answer 1

$(2^x+2^{-x})^3=3^3 \\ \\ 2^{3x}+3.2^{2x}.2^{-x}+3.2^x.2^{-2x}+2^{-3x}=27 \\ \\ 2^{3x}+3.2^{x}+3.2^{-x}+2^{-3x}=27 \\ \\ 2^{3x}+2^{-3x}+3(2^x+2^{-x})=27 \\ \\ 2^{3x}+2^{-3x}+3.3=27 \\ \\ 2^{3x}+2^{-3x}+9=27 \\ \\ 2^{3x}+2^{-3x}=18 \\ \\ 8^x+8^{-x}=18$