Respostas

2014-07-22T19:06:19-03:00
Olá Julie,

use as propriedades da exponenciação:

a^{m+n}~\to~a^m*a^n\\\\
a^{-m}~\to~ \dfrac{1}{a^m}

______________________

5^x+5^{-x}=5^{1-x}-3\\\\
5^x+ \dfrac{1}{5^x}=5^1*5^{-x}-3\\\\
5^x+ \dfrac{1}{5^x}=5* \dfrac{1}{5^x}-3\\\\
5^x=k\\\\
k+ \dfrac{1}{k}=5* \dfrac{1}{k}-3\\\\
 \dfrac{k^2+1}{\not k}= \dfrac{5}{\not k}- \dfrac{3k}{\not k}\\\\
k^2+1=5-3k\\
k^2+3k-4=0

\Delta=b^2-4ac\\
\Delta=3^2-4*1*(-4)\\
\Delta=9+16\\
\Delta=25\\\\
k= \dfrac{-b\pm \sqrt{\Delta} }{2a}= \dfrac{-3\pm \sqrt{25} }{2*1}= \dfrac{-3\pm5}{2}\begin{cases}k'= \dfrac{-3+5}{2}= \dfrac{2}{2}=1\\\\
k''= \dfrac{-3-5}{2}= \dfrac{-8}{~~2}=-4\notin\mathbb{R} \end{cases}\\\\\\
5^x=k\\
5^x=1\\
5^x=5^0\\
\not5^x=\not5^0\\\\
x=0\\\\\\
\boxed{S=\{0\}}

Espero ter ajudado e tenha ótimos estudos =))
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