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$1)\,\,\,y - x = 2\,\,\,\, \Leftrightarrow \,\,\,y = x + 2$
Do đó ${3^x}{.2^y} = \frac{1}{9}\,\,\,\, \Leftrightarrow \,\,{3^x}{.2^{x + 2}} = \frac{1}{9}\,\,\,\, \Leftrightarrow {6^x} = \frac{1}{{36}}$
$ \Leftrightarrow {6^x} = {6^{ - 2}}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,x = - 2$ suy ra $y = 0$
Vậy hệ có nghiệm là $( - 2,0)$
$2)$
$\begin{array}{l}
\,\,\,\,\,\,\,x + y = 1\,\,\,\, \Leftrightarrow y = 1 - x\\
\,\,\,\,\,\,\left\{ \begin{array}{l}
{2^y} = {200.5^x}\\
x + y = 1
\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \left\{ \begin{array}{l}
{2^{1 - x}} = {200.5^x}\\
y = 1 - x
\end{array} \right.\,\,\,\,\, \Leftrightarrow \left\{ \begin{array}{l}
{10^{ - x}} = {10^2}\\
y = 1 - x
\end{array} \right.\\
\Leftrightarrow \,\left\{ \begin{array}{l}
x = - 2\\
y = 3
\end{array} \right.
\end{array}$
Vậy hệ có nghiệm $( - 2,3)$
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Đăng bài 26-04-12 03:52 PM
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