Giải các bất phương trình :

$\begin{array}{l}
1)\left| x - 1 \right|^{\log^2x - \log x^2} \ge \left| x - 1 \right|^3         (1)\\
2)\left| x \right|^{x^2 - 2x} \ge 1                                   (2)
\end{array}$
$1)\,\,\,x = 1$ vế trái không xác định, ĐK:$x > 0$
•    $\left| {x - 1} \right| > 1\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \left[ \begin{array}{l}
 x > 2\\
 x < 0
\end{array} \right.$    (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 $\frac{1}{{10}} \le x \le 2$
                                          ĐS:  $\left[ \begin{array}{l}
\frac{1}{{10}} \le x < 2\\
x \ge 1000
\end{array} \right.$
$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 $0 < x < 1$
ĐS : $\left[ \begin{array}{l}
x <  - 1\\
0 < x < 1\\
x \ge 2
\end{array} \right.$
rất cám ơn bạn đã giải giúp mình –  langtu_sitinh_dangyeuxxx 11-07-12 01:17 PM
những bài này mình cũng sợ lắm. Nhưng làm nhiều giờ cũng đỡ sợ hơn rồi hihi –  emometri 11-07-12 01:10 PM
mình cứ nhìn hàm log là phát sợ rồi –  anh_chang_zaizai_90 11-07-12 01:02 PM
Gửi bạn lời giải.Bạn xem chỗ nào mà không hiểu cứ hỏi mình nhé –  Tiểu Bắc 11-07-12 12:41 PM

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