Giải các bất phương trình
a/ $5 x^{2} . 4^{8 x^{2} +3x}+8x+ 2^{16 x^{2} +6x } > 10 x^{2} +2 +x. 4^{8 x^{2} +3x+1}$
b/ $3^{2x}-8. 3^{x+ \sqrt{ x+4}} – 9^{ \sqrt{ x+4}+1}>0$
c/ $4^{x} \leq 3.2^{x+ \sqrt{ x}} +4^{1+ \sqrt{ x}}$
d/ $4 x^{2} + 3^{ \sqrt{ x}+1}+x.3^{ \sqrt{ x}}< 2 x^{2} . 3^{ \sqrt{ x}} +2x+6$
a/ $5 x^{2} . 4^{8 x^{2} +3x}+8x+ 2^{16 x^{2} +6x } > 10 x^{2} +2 +x. 4^{8 x^{2} +3x+1}$
$\Leftrightarrow 4^{8 x^{2} +3x} \left(  5 x^{2} -4x+1  \right) – 2 \left( 5 x^{2} -4x+1   \right) >0$
$\Leftrightarrow \left(   5 x^{2} -4x+1    \right) \left( 4^{8 x^{2} +3x}-2   \right)>0 $
$\Leftrightarrow  4^{8 x^{2} +3x}-2   >0$ do $5 x^{2} -4x+1    >0  \forall x, \Delta=1>0$
$\Leftrightarrow  4^{8 x^{2} +3x}>2   \Leftrightarrow  4^{8 x^{2} +3x}> 4^{\frac{  1}{2}}   $
$\Leftrightarrow 8 x^{2} +3x> \frac{ 1}{2}$ (do 4>0)
$\Leftrightarrow 16 x^{2} +6x -1 >0 \Leftrightarrow x < - \frac{ 1}{2}$ hay $x> \frac{ 1}{8}$
Vậy bất phương trình có nghiệm $x\in \left ( -\infty;-\frac{1}{2} \right )\cup \left ( \frac{1}{8} ;+\infty \right )$

b/ $3^{2x}-8. 3^{x+ \sqrt{ x+4}} – 9^{ \sqrt{ x+4}+1}>0$ điều kiện: $x \geq -4$
$\Leftrightarrow 3^{2x}-8. 3^{ \sqrt{ x+4}}.3^{x}-9.9^{\sqrt{ x+4}}>0$
Đặt $3^{x}=t, t>0: t^{2}-8.3^{ \sqrt{ x+4}}.t -9. 9^{ \sqrt{ x+4}}>0$
Vế trái là tam thức của t có $\Delta ‘= \left(4.3^{ \sqrt{ x+4}}   \right)^{2} +9. 9^{ \sqrt{ x+4}}= 16. 9^{ \sqrt{ x+4}}+9. 9^{ \sqrt{ x+4}}= 25.9^{ \sqrt{ x+4}} $
$\Rightarrow \sqrt{ \Delta ‘}=5. 3^{ \sqrt{ x+4}}$
$\Rightarrow  \left[ \begin{array}{l} t=4.3^{ \sqrt{ x+4}}-5. 3^{ \sqrt{ x+4}}=-2. 3^{ \sqrt{ x+4}}<0 (L)  \\ t=4. 3^{ \sqrt{ x+4}}+5. 3^{ \sqrt{ x+4}}=9. 3^{ \sqrt{ x+4}}=3^{2+ \sqrt{ x+4}}   \end{array} \right. $
$\Rightarrow 3^{x} >3^{ 2+\sqrt{ x+4}} \Leftrightarrow  x>2+ \sqrt{ x+4} \Leftrightarrow x-2 > \sqrt{ x+4} $
$\Leftrightarrow \begin{cases}x \geq 2    \\ x^{2} -4x+4 > x+4    \end{cases}  \Leftrightarrow \begin{cases}  x \geq 2  \\  x^{2} -5x >0   \end{cases} \Leftrightarrow \begin{cases} x \geq 2   \\   x<0, x>5  \end{cases} \Leftrightarrow x>5 $
Vậy bất phương trình có nghiệm x>5. 

c/ $4^{x} \leq 3.2^{x+ \sqrt{ x}} +4^{1+ \sqrt{ x}}$
Điều kiện: $x \geq 0$
Bất phương trình $\Leftrightarrow  \frac{ 2^{2x}}{2^{x+ \sqrt{ x}}} \leq 3+ \frac{ 2^{2+2 \sqrt{ x}}}{2^{x+ \sqrt{ x}}} \Leftrightarrow 2^{x+ \sqrt{ x}} \leq 3+2^{2}. 2^{ \sqrt{ x}-x}$
Đặt $2^{x- \sqrt{ x} }=t, t>0 \Rightarrow 2^{ \sqrt{ x}-x}= \frac{ 1}{2^{ x-\sqrt{ x}}}$
$t \leq 3+ \frac{ 4}{t} \Leftrightarrow t^{2}-3t-4 \leq 0$
$\Leftrightarrow -1 \leq t \leq 4 \Leftrightarrow 0 <t \leq 4$
$\Leftrightarrow 2^{ x-\sqrt{ x}} \leq 0 \Leftrightarrow -1 \leq \sqrt{ x}  \leq 2$
$\Leftrightarrow  0 \leq \sqrt{ x} \leq 2 \Leftrightarrow 0 \leq x \leq 4$
Vậy bất phương trình có nghiệm $0\leq x\leq 4.$ 

d/ $4 x^{2} + 3^{ \sqrt{ x}+1}+x.3^{ \sqrt{ x}}< 2 x^{2} . 3^{ \sqrt{ x}} +2x+6$
Điều kiện: $x \geq 0$
Bất phương trình $\Leftrightarrow 4 x^{2} – 2x -6 <3^{ \sqrt{ x}} \left( 2 x^{2} –x -3   \right) $
$\Leftrightarrow \left(  2 x^{2} –x -3   \right) \left(3^{ \sqrt{ x}}-2    \right) >0$
$\Rightarrow $ nghiệm của phương trình: $0 \leq x < \log_{3^{2} }{2} $ hay $x> \frac{ 3}{2}$

Thẻ

Lượt xem

789
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