Question

9^(x-1/2) - 4/3^(1-x) = -1 como resolver?

Answer 1

$9^{x- \frac{1}{2} } - \frac{4}{3^{1-x}} = -1 \\ \\ (3^{2})^{x- \frac{1}{2} } - 4.3^{-(1-x)}=-1 \\ \\ 3^{2x - 1}-4.3^{x-1}=-1 \\ \\ \frac{3^{2x}}{3}-4. \frac{3^{x}}{3} =-1 \\ \\ 3^{2x} - 4.3^{x} = -3 \\ \\ y = 3^{x} \\ \\ y^{2}-4.y + 3 = 0 \\ \\ D = (-4)^{2}-4(1)(3) = 16-12 = 4 \\ \\ \sqrt{D} = 2 \\ \\ y' = \frac{(4+2)}{2} = 3 \\ \\ y'' = \frac{(4-2)}{2} = 1 \\ \\ y = 3^{x} \\ \\ 3 = 3^{x} -\ \textgreater \ x = 1 \\ \\ 1 = 3^{x}-\ \textgreater \ 3^{0}=3^{x}-\ \textgreater \ x = 0$

Resposta: x = 0 ou x = 1

Espero ter ajudado.