Question

urgente me ajudem nessa equaçao
2 elevado a x + 1 + 2 elevado a 1 - x - 5 = 0 ​

Answer 1

Sua questão dá dupla interpretação.

1º ${2}^{x+1}+{2}^{1-x}-5=0$

2º ${2}^{x+1}+{2}^{1-x-5}=0$

Vou resolver das duas formas!

${2}^{x+1} +{2}^{1-x}-5=0$

${2}^{x}. {2}^{1}+\frac{{2}^{1}}{{2}^{x}}=5$

faça ${2}^{x}=y$

$2y+\frac{2}{y}=5\\2{y}^{2}-5y+2=0$

$\Delta=25-16=9$

$y=\frac{5±3}{2}$

$y'=4\\y''=1$

${2}^{x}=y$

${2}^{x}=4$

${2}^{x}={2}^{2}$

$\boxed{\boxed{x=2}}$

${2}^{x}=y$

${2}^{x}=1 \\{2}^{x}={2}^{0}$

$\boxed{\boxed{x=0}}$

**************************//*************************************

${2}^{x+1}+{2}^{1-x-5}=0$

${2}^{x+1}+{2}^{-4-x}=0$

${2}^{x}. {2}^{1}+\frac{{2}^{-4}}{{2}^{x}}=0$

faça ${2}^{x}=y$

$2y+\frac{1}{16y}=0\times16y \\ 32{y}^{2}+1=0$

$32{y}^{2}=-1 \\ {y}^{2}=-\frac{1}{32}$

S=∅