Respostas

2014-08-20T23:37:01-03:00
Faço : 3^x=y --->  (3^x)²-28.(3^x)=27=0 ====> y²-28y-27=0
a partir disso se resolve a equação e depois para os valores encontrados substitui em 3^x=y! Abraços
1 5 1
A melhor resposta!
2014-08-21T01:07:12-03:00
Oi ^^

9^x-28\cdot3^x+27=0~~.\\
(3^2)^x-28\cdot3^x+27=0~~.\\
(3^x)^2-28\cdot3^x+27=0\\\\
fazendo~3^x=m\\\\
(m)^2-28\cdot(m)+27=0\\
m^2-28m+27=0\\\\
\Delta=b^2-4ac\\
\Delta=(-28)^2-4\cdot1\cdot27~~.\\
\Delta=784-108\\
\Delta=676\\\\
m= \dfrac{-b\pm \sqrt{\Delta} }{2a}= \dfrac{-(-28)\pm \sqrt{676} }{2\cdot1}= \dfrac{28\pm26}{2}\\\\\\
\begin{cases}m'=\dfrac{28-26}{2}= \dfrac{2}{2}=1\\\\
m''=\dfrac{28+26}{2}=\dfrac{54}{2}=27    \end{cases}

Retomando a variável original, 3^x=m:

3^x=1~~~~~~~~~~~~~~~~~~~~~~~~3^x=27\\
3^x=3^0~~~~~~~~~~~~~~~~~~~~~~~3^x=3^3\\
\not3^x=\not3^0~~~~~~~~~~~~~~~~~~~~~~\not3^x=\not3^3\\\\
x'=0~~~~~~~~~~~~~~~~~~~~~~~~~x''=3\\\\\\
\Large\boxed{\boxed{\boxed{S=\{0,3\}}}}.\\.

Ótimos estudos ;D
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