Question

Com 2x+2-x=3 , qual o valor numérico de 4x+4-x (Obs: os ultimos -x estão elevados)

Answer 1

$2^x+2^{-x}=3\\ \\2^x+ \frac{1}{2^x} =3\\ \\\left(2^x+ \frac{1}{2^x}\right)^2 =3^2\\ \\(2^x)^2+2\cdot2^x\cdot \frac{1}{2^x}+\left(\frac{1}{2^x}\right)^2 =9\\ \\(2^2})^x+2+\left(\frac{1}{2^2}\right)^x =9\\ \\(4})^x+\left(\frac{1}{4}\right)^x =9-2\\ \\4^x+\frac{1}{4^x} =9-2\\ \\4^x+\frac{1}{4^x} =7\\ \\4^x+4^{-x} =7$