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$ (1)$$ \Leftrightarrow \sqrt {5 - x} > 3 - x > 0\,\,\,\,\, \Leftrightarrow \,\,\,\,\left\{ \begin{array}{l}
5 - x > {\left( {3 - x} \right)^2}\\
x < 3
\end{array} \right.$
$ \Leftrightarrow \,\left\{ \begin{array}{l}
{x^2} - 5x + 4 < 0\\
x < 3
\end{array} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,1 < x < 3$
$(2)$
$ \Leftrightarrow \,\,x = k - \frac{1}{3}$
Do đó : $1 < k - \frac{1}{3} < 3\,\,\, \Leftrightarrow \,\,\,\frac{4}{3} < k < \frac{{10}}{3}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\left[ \begin{array}{l}
k = 2\\
k = 3
\end{array} \right.$
- Với $k = 2:\,\,\,x = 2 - \frac{1}{3} = \frac{5}{3}$
- Với $k = 3:\,\,\,x = 3 - \frac{1}{3} = \frac{8}{3}$
Vậy $\left[ \begin{array}{l}
x = \frac{5}{3}\\
x = \frac{8}{3}
\end{array} \right.$
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Đăng bài 26-04-12 05:04 PM
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