Question

x.(x-\(\frac{1}{2}\))<0                              \(\frac{x-1}{x+2}\)  <0

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Answer 1

Lời giải:
a.

$x(x-\frac{1}{2})< 0$
\(\Leftrightarrow \left[\begin{matrix} \left\{\begin{matrix} x< 0\\ x-\frac{1}{2}>0\end{matrix}\right.\\ \left\{\begin{matrix} x>0\\ x-\frac{1}{2}< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} 0> x>\frac{1}{2} (\text{vô lý})\\ 0< x< \frac{1}{2}(\text{chọn})\end{matrix}\right.\)

b.

\(\frac{x-1}{x+2}< 0\Leftrightarrow \left[\begin{matrix} \left\{\begin{matrix} x-1< 0\\ x+2>0\end{matrix}\right.\\ \left\{\begin{matrix} x-1>0\\ x+2< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} -2< x< 1(\text{chọn})\\ -2> x>1(\text{vô lý})\end{matrix}\right.\)