Giải các bất phương trình :
$\begin{array}{l}
1)\log _x2.\log _{2x}2 > \log _{4x}2                         (1)\\
2)\log _{\left| x \right|}\left( {x^2 - \frac{1}{2}x} \right) > 1                            (2)
\end{array}$
1) Điều kiện:
$\,\,\,x > 0,\,\,\,x \ne 1,\,\,x \ne \frac{1}{2},\,\,x \ne \frac{1}{4}$
Khi đó ta có
$(1) \Leftrightarrow \frac{1}{{{{\log }_2}x}}.\frac{1}{{1 + {{\log }_2}x}} > \frac{1}{{2 + {{\log }_2}x}}$  
Đặt $u = {\log _2}x,$ ta có: $\begin{array}{l}
\frac{1}{u}.\frac{1}{{1 + u}} > \frac{1}{{2 + u}}\\

\end{array}$
$ \Leftrightarrow \frac{{2 - {u^2}}}{{u\left( {1 + u} \right)\left( {2 + u} \right)}} > 0\,\,\,\,\,\,\,\,(1');$
Xét dấu vế trái, đặt $f(u)$, bằng phương pháp khoảng

Nghiệm của $(1')$là: $\left[ \begin{array}{l}
u <  - 2\\
- \sqrt 2  < u <  - 1\\
0 < u < \sqrt 2
\end{array} \right.$
Suy ra $\left[ \begin{array}{l}
{\log _2}x <  - 2\\
 - \sqrt 2  < {\log _2}x <  - 1\\
0 < {\log _2}x < \sqrt 2
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
0 < x < \frac{1}{4}\\
\frac{1}{{{2^{\sqrt 2 }}}} < x < \frac{1}{2}\\
1 < x < {2^{\sqrt 2 }}
\end{array} \right.$
Tập nghiệm của BPT là:
$S=\left (0;\frac{1}{4} \right )\cup \left (\frac{1}{2^\sqrt2};\frac{1}{2} \right )\cup \left (1;2^\sqrt2\right )$

$2)$
Điều kiện:$\left\{ \begin{array}{l}
x \ne 0\\
x \ne  \pm 1\\
x < 0\,\,\,\,;\,\,\,\,x > \frac{1}{2}
\end{array} \right.$
Xét $2$ trường hợp :
$a)\left\{ \begin{array}{l}
\left| x \right| < 1\\
x \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
 - 1 < x < 1\\
x \ne 0
\end{array} \right.$  khi đó $(2) \Leftrightarrow 0 < {x^2} - \frac{1}{2}x < \left| x \right|$
Suy ra      $\left[ \begin{array}{l}
 - \frac{1}{2} < x < 0\\
\frac{1}{2} < x < 1
\end{array} \right.$
$b)$  $\left| x \right| > 1 \Leftrightarrow \left[ \begin{array}{l}
x > 1\\
x <  - 1
\end{array} \right.$
với
$\begin{array}{l}
x > 1:\,\,(2) \Leftrightarrow {x^2} - \frac{1}{2}x > x\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow {x^2} - \frac{3}{2}x \Leftrightarrow x > \frac{3}{2}
\end{array}$
Với $x <  - 1:(2) \Leftrightarrow {x^2} - \frac{1}{2}x >  - x$
                       $ \Leftrightarrow {x^2} + \frac{1}{2}x > 0\,\,\,\,\, \Leftrightarrow x <  - 1$
Tập nghiệm của $(2)$ là:
$\begin{array}{l}
S = ( - \infty , - 1) \cup ( - \frac{1}{2},0) \cup (\frac{1}{2},1) \cup (\frac{3}{2}, + \infty )\\

\end{array}$
cam on ban Ad nhieu nhe –  anh_chang_zaizai_90 12-07-12 09:25 PM
Gui ban tham khao nhe –  Tiểu Bắc 12-07-12 09:14 PM

Bạn cần đăng nhập để có thể gửi đáp án

Chat chit và chém gió
  • Việt EL: ... 8/21/2017 8:20:01 AM
  • Việt EL: ... 8/21/2017 8:20:03 AM
  • wolf linhvân: 222 9/17/2017 7:22:51 AM
  • dominhdai2k2: u 9/21/2017 7:31:33 AM
  • arima sama: helllo m 10/8/2017 6:49:28 AM
  • ๖ۣۜGemღ: Mọi người có thắc mắc hay cần hỗ trợ gì thì gửi tại đây nhé https://goo.gl/dCdkAc 12/6/2017 8:53:25 PM
  • anhkind: hi mọi người mk là thành viên mới nè 12/28/2017 10:46:02 AM
  • anhkind: party 12/28/2017 10:46:28 AM
  • Rushia: . 2/27/2018 2:09:24 PM
  • Rushia: . 2/27/2018 2:09:25 PM
  • Rushia: . 2/27/2018 2:09:25 PM
  • Rushia: . 2/27/2018 2:09:26 PM
  • Rushia: . 2/27/2018 2:09:26 PM
  • Rushia: . 2/27/2018 2:09:26 PM
  • Rushia: . 2/27/2018 2:09:26 PM
  • Rushia: . 2/27/2018 2:09:27 PM
  • Rushia: . 2/27/2018 2:09:27 PM
  • Rushia: . 2/27/2018 2:09:28 PM
  • Rushia: . 2/27/2018 2:09:28 PM
  • Rushia: . 2/27/2018 2:09:28 PM
  • Rushia: . 2/27/2018 2:09:29 PM
  • Rushia: . 2/27/2018 2:09:29 PM
  • Rushia: . 2/27/2018 2:09:29 PM
  • Rushia: . 2/27/2018 2:09:29 PM
  • Rushia: . 2/27/2018 2:09:30 PM
  • Rushia: . 2/27/2018 2:09:30 PM
  • Rushia: . 2/27/2018 2:09:31 PM
  • Rushia: .. 2/27/2018 2:09:31 PM
  • Rushia: . 2/27/2018 2:09:32 PM
  • Rushia: . 2/27/2018 2:09:32 PM
  • Rushia: . 2/27/2018 2:09:32 PM
  • Rushia: . 2/27/2018 2:09:32 PM
  • Rushia: . 2/27/2018 2:09:33 PM
  • Rushia: . 2/27/2018 2:09:33 PM
  • Rushia: . 2/27/2018 2:09:33 PM
  • Rushia: . 2/27/2018 2:09:34 PM
  • ๖ۣۜBossღ: c 3/2/2018 9:20:18 PM
  • nguoidensau2k2: hello 4/21/2018 7:46:14 PM
  • ☼SunShine❤️: Vẫn vậy <3 7/31/2018 8:38:39 AM
  • ☼SunShine❤️: Bên này text chữ vẫn đẹp nhất <3 7/31/2018 8:38:52 AM
  • ☼SunShine❤️: @@ lại càng đẹp <3 7/31/2018 8:38:59 AM
  • ☼SunShine❤️: Hạnh phúc thế sad mấy câu hỏi vớ vẩn hồi trẩu vẫn hơn 1k xem 7/31/2018 8:41:00 AM
  • tuyencr123: vdfvvd 3/6/2019 9:30:53 PM
  • tuyencr123: dv 3/6/2019 9:30:53 PM
  • tuyencr123: d 3/6/2019 9:30:54 PM
  • tuyencr123: dv 3/6/2019 9:30:54 PM
  • tuyencr123: d 3/6/2019 9:30:54 PM
  • tuyencr123: d 3/6/2019 9:30:55 PM
  • tuyencr123: đ 3/6/2019 9:30:55 PM
  • tuyencr123: đ 3/6/2019 9:30:56 PM
  • tuyencr123: d 3/6/2019 9:30:56 PM
  • tuyencr123: d 3/6/2019 9:30:56 PM
  • tuyencr123: d 3/6/2019 9:30:56 PM
  • tuyencr123: d 3/6/2019 9:30:56 PM
  • tuyencr123: d 3/6/2019 9:30:56 PM
  • tuyencr123: d 3/6/2019 9:30:57 PM
  • tuyencr123: d 3/6/2019 9:30:57 PM
  • tuyencr123: d 3/6/2019 9:30:57 PM
  • tuyencr123: d 3/6/2019 9:30:57 PM
  • tuyencr123: d 3/6/2019 9:30:57 PM
  • tuyencr123: d 3/6/2019 9:30:58 PM
  • tuyencr123: đ 3/6/2019 9:30:58 PM
  • tuyencr123: d 3/6/2019 9:30:58 PM
  • tuyencr123: d 3/6/2019 9:30:58 PM
  • tuyencr123: d 3/6/2019 9:30:59 PM
  • tuyencr123: d 3/6/2019 9:30:59 PM
  • tuyencr123: d 3/6/2019 9:30:59 PM
  • tuyencr123: d 3/6/2019 9:30:59 PM
  • tuyencr123: d 3/6/2019 9:30:59 PM
  • tuyencr123: d 3/6/2019 9:31:00 PM
  • tuyencr123: d 3/6/2019 9:31:00 PM
  • tuyencr123: d 3/6/2019 9:31:00 PM
  • tuyencr123: d 3/6/2019 9:31:00 PM
  • tuyencr123: đ 3/6/2019 9:31:01 PM
  • tuyencr123: d 3/6/2019 9:31:01 PM
  • tuyencr123: đ 3/6/2019 9:31:01 PM
  • tuyencr123: d 3/6/2019 9:31:02 PM
  • tuyencr123: d 3/6/2019 9:31:02 PM
  • tuyencr123: d 3/6/2019 9:31:02 PM
  • tuyencr123: d 3/6/2019 9:31:02 PM
  • tuyencr123: d 3/6/2019 9:31:02 PM
  • tuyencr123: d 3/6/2019 9:31:03 PM
  • tuyencr123: d 3/6/2019 9:31:03 PM
  • tuyencr123: d 3/6/2019 9:31:03 PM
  • tuyencr123: d 3/6/2019 9:31:03 PM
  • tuyencr123: d 3/6/2019 9:31:04 PM
  • tuyencr123: d 3/6/2019 9:31:04 PM
  • tuyencr123: d 3/6/2019 9:31:04 PM
  • tuyencr123: d 3/6/2019 9:31:04 PM
  • tuyencr123: d 3/6/2019 9:31:05 PM
  • tuyencr123: đ 3/6/2019 9:31:05 PM
  • tuyencr123: bb 3/6/2019 9:31:06 PM
  • tuyencr123: b 3/6/2019 9:31:06 PM
  • tuyencr123: b 3/6/2019 9:31:06 PM
  • tuyencr123: b 3/6/2019 9:31:07 PM
  • tuyencr123: b 3/6/2019 9:31:38 PM
  • Tríp Bô Hắc: cho hỏi lúc đăng câu hỏi em có thấy dòng cuối là tabs vậy ghi gì vào tabs vậy ạ 7/15/2019 7:36:37 PM
  • khanhhuyen2492006: hi 3/19/2020 7:33:03 PM
  • ngoduchien36: hdbnwsbdniqwjagvb 11/17/2020 2:36:40 PM
  • tongthiminhhangbg: hello 6/13/2021 2:22:13 PM
Đăng nhập để chém gió cùng mọi người
  • hoàng anh thọ
  • Thu Hằng
  • Xusint
  • HọcTạiNhà
  • lilluv6969
  • ductoan933
  • Tiến Thực
  • my96thaibinh
  • 01668256114abc
  • Love_Chishikitori
  • meocon_loveky
  • gaprodianguc95
  • smallhouse253
  • hangnguyen.hn95.hn
  • nguyencongtrung9744
  • tart
  • kto138
  • dphonglkbq
  • ๖ۣۜPXM๖ۣۜMinh4212♓
  • huyhieu10.11.1999
  • phungduyen1403
  • lalinky.ltml1212
  • trananhvan12315
  • linh31485
  • thananh133
  • Confusion
  • Hàn Thiên Dii
  • •♥•.¸¸.•♥•Furin•♥•.¸¸.•♥•
  • dinhtuyetanh000
  • LeQuynh
  • tuanmotrach
  • bac1024578
  • truonglinhyentrung
  • Lê Giang
  • Levanbin147896325
  • anhquynhthivu
  • thuphuong30012003