|
|
1)ĐK:$x > 0$
• $x = 1$ vế trái không xác định.
• $\left| {x - 1} \right| > 1\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \left[ \begin{array}{l}
x > 2\\
x < 0
\end{array} \right.$ (loại $x < 0$)
$(1) \Leftrightarrow {\log ^2}x - \log {x^2} \ge 3 \Leftrightarrow \left[ \begin{array}{l}
\log x \le - 1\\
\log x \ge 3
\end{array} \right.\,\,\,\, \Leftrightarrow \left[ \begin{array}{l}
x \le \frac{1}{{10}}\\
x \ge 1000
\end{array} \right.$
Do $x > 2$ nên $x \ge 1000$.
• $\left| {x - 1} \right| < 1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,0 < x < 2$
$\begin{array}{l}
(1) \Leftrightarrow {\log ^2}x - 2\log x - 3 \le 0\,\,\, \Leftrightarrow \,\, - 1 \le \log x \le 3\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \frac{1}{{10}} \le x \le 1000
\end{array}$
Do $0 < x < 2$ nên $\frac{1}{{10}} \le x \le 2$
Vây BPT đã cho có nghiệm:
$\left[ \begin{array}{l}
\frac{1}{{10}} \le x < 2\\
x \ge 1000
\end{array} \right.$
$2)$
• $x = 0$ vế trái không xác định
$\begin{array}{l}
• \left| x \right| > 1:(2) \Leftrightarrow {x^2} - 2x \ge 0\,\,\,\,\,\, \Leftrightarrow \left[ \begin{array}{l}
x \le 0\\
x \ge 2
\end{array} \right.\\
\end{array}$
Do $\left| x \right| > 1$ nên $\left[ \begin{array}{l}
x < - 1\\
x \ge 2
\end{array} \right.$
• $\left| x \right| < 1,\,\,x \ne 0\,\,\,(1) \Leftrightarrow {x^2} - 2x \le 0\,\,\, \Leftrightarrow 0 < x \le 2$
Do $\left\{ \begin{array}{l}
- 1 < x < 1\\
x \ne 0
\end{array} \right.\,\,\,\,$nên $0 < x < 1$
Vây BPT đã cho có nghiệm:
$\left[ \begin{array}{l}
x < - 1\\
0 < x < 1\\
x \ge 2
\end{array} \right.$
|