Giải bpt sau: \(\frac{\left|x^2-4x+3\right|-x-3}{x+3}\le2x\)
Giúp mình nha :(((
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Giải BPT sau giúp mik vs T_T
\(\dfrac{3\left(4x^2-9\right)}{\sqrt{3x^2-3}}\le2x+3\)
ĐKXĐ: \(\left[{}\begin{matrix}x>1\\x< -1\end{matrix}\right.\)
- Với \(x=-\dfrac{3}{2}\) là nghiệm của BPT
- Với \(x>-\dfrac{3}{2}\Rightarrow2x+3>0\)
\(\Rightarrow\dfrac{3\left(2x-3\right)\left(2x+3\right)}{\sqrt{3x^2-3}}\le2x+3\)
\(\Leftrightarrow\dfrac{3\left(2x-3\right)}{\sqrt{3x^2-3}}\le1\)
\(\Rightarrow3\left(2x-3\right)\le\sqrt{3x^2-3}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3< 0\\\left\{{}\begin{matrix}2x-3\ge0\\9\left(2x-3\right)^2\le3x^2-3\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{3}{2}< x< \dfrac{3}{2}\\\left[{}\begin{matrix}x\ge\dfrac{3}{2}\\11x^2-36x+28\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-\dfrac{3}{2}< x< \dfrac{3}{2}\\\left\{{}\begin{matrix}x\ge\dfrac{3}{2}\\\dfrac{14}{11}\le x\le2\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}-\dfrac{3}{2}< x< \dfrac{3}{2}\\\dfrac{3}{2}\le x\le2\end{matrix}\right.\) \(\Rightarrow-\dfrac{3}{2}< x\le2\)
Kết hợp ĐKXĐ \(\Rightarrow\left[{}\begin{matrix}-\dfrac{3}{2}< x< -1\\1< x\le2\end{matrix}\right.\)
- Với \(x< -\dfrac{3}{2}\Rightarrow2x+3< 0\)
\(\dfrac{3\left(2x-3\right)\left(2x+3\right)}{\sqrt{3x^2-3}}\le2x+3\Leftrightarrow\dfrac{3\left(2x-3\right)}{\sqrt{3x^2-3}}\ge1\)
\(\Rightarrow3\left(2x-3\right)\ge\sqrt{3x^2-3}\)
Do \(x< -\dfrac{3}{2}\Rightarrow3\left(2x-3\right)< 0\Rightarrow\) BPT vô nghiệm
Vậy nghiệm của BPT là \(\left[{}\begin{matrix}-\dfrac{3}{2}\le x< -1\\1< x\le2\end{matrix}\right.\)
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giải các hệ BPT sau:
a) left{{}begin{matrix}5x-24x+55x-4 x+2end{matrix}right.
b) left{{}begin{matrix}2x+13x+45x+3ge8x-9end{matrix}right.
c) left{{}begin{matrix}frac{5x+2}{3}ge4-xfrac{6-5x}{13} 3x+1end{matrix}right.
d) left{{}begin{matrix}frac{4x-5}{7} x+3frac{3x+8}{4}2x-5end{matrix}right.
e) left{{}begin{matrix}6x+frac{5}{7} 4x+7frac{8x+3}{2} 2x+5end{matrix}right.
f) left{{}begin{matrix}15x-22x+frac{1}{3}2left(x-4right) frac{3x-14}{2}end{matrix}right.
g) left{{}begin{matrix}x-1le2x-33x x+...
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giải các hệ BPT sau:
a) \(\left\{{}\begin{matrix}5x-2>4x+5\\5x-4< x+2\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}2x+1>3x+4\\5x+3\ge8x-9\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\frac{5x+2}{3}\ge4-x\\\frac{6-5x}{13}< 3x+1\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}\frac{4x-5}{7}< x+3\\\frac{3x+8}{4}>2x-5\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}6x+\frac{5}{7}< 4x+7\\\frac{8x+3}{2}< 2x+5\end{matrix}\right.\)
f) \(\left\{{}\begin{matrix}15x-2>2x+\frac{1}{3}\\2\left(x-4\right)< \frac{3x-14}{2}\end{matrix}\right.\)
g) \(\left\{{}\begin{matrix}x-1\le2x-3\\3x< x+5\\5-3x\le2x-6\end{matrix}\right.\)
h) \(\left\{{}\begin{matrix}2x+\frac{3}{5}>\frac{3\left(2x-7\right)}{3}\\x-\frac{1}{2}< \frac{5\left(3x-1\right)}{2}\end{matrix}\right.\)
j) \(\left\{{}\begin{matrix}\frac{3x+1}{2}-\frac{3-x}{3}\le\frac{x+1}{4}-\frac{2x-1}{3}\\3-\frac{2x+1}{5}>x+\frac{4}{3}\end{matrix}\right.\)
https://i.imgur.com/NOxfqjV.jpg
https://i.imgur.com/awOKwJi.jpg
https://i.imgur.com/a0ApmAE.jpg
Giải bpt sau: \(\left|2x+3\right|\le2x^2-x-2\)
giúp mình với !!!
- Với \(x\ge-\frac{3}{2}\)
\(\Leftrightarrow2x^2-x-2\ge2x+3\)
\(\Leftrightarrow2x^2-3x-5\ge0\Rightarrow\left[{}\begin{matrix}x\le-1\\x\ge\frac{5}{3}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}-\frac{3}{2}\le x\le-1\\x\ge\frac{5}{3}\end{matrix}\right.\)
- Với \(x< -\frac{3}{2}\)
\(\Leftrightarrow2x^2-x-2\ge-2x-3\)
\(\Leftrightarrow2x^2+x+1\ge0\) (luôn đúng)
Vậy nghiệm của BPT là \(\left[{}\begin{matrix}x\le-1\\x\ge\frac{5}{3}\end{matrix}\right.\)
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1.giải các bpt sau
a.\(\left(x-3\right)\left(x+3\right)\ge x^2-7x+1\)
b.\(\dfrac{1,5-x}{5}\ge\dfrac{4x+5}{2}\)
2.giải các pt sau
\(x^3+1=x.\left(x+1\right)\)
Giải bpt
\(\frac{\left|x^2-4x\right|+3}{x^2+\left|x-5\right|}\ge1\)
giải bpt
\(\left(\sqrt{x+4}-1\right)\sqrt{x+2}\ge\frac{x^3+4x^2+3x-2\left(x+3\right)\sqrt[3]{2x+3}}{\left(\sqrt[3]{2x+3}-3\right)\left(\sqrt{x+4}+1\right)}\)
Giải bpt sau:
\(\frac{\left(x-1\right)^3\left(x+2\right)^4\left(x-3\right)^5\left(x+6\right)}{x^2\left(x-7\right)^3}\le0\)
Giải phương trình :
1)\(\sqrt[3]{6x+1}=8x^3-4x-1\\ \)
2)\(2x+\frac{x-1}{x}=\sqrt[2]{1-\frac{1}{x}}+3\sqrt{x-\frac{1}{x}}\)
3)\(\frac{15}{2}\left(30x^2-4x\right)=2004\left(\sqrt{30060x+1}+1\right)\)
Ai biết giải giúp mình nha,mình nổ não lun mà ko giải được.
Giải bpt:
a,\(\frac{\sqrt{x^2-x+4}-2x-3}{x-2}>3\)
b, \(\sqrt{x\left(x-1\right)}+\sqrt{x\left(x+2\right)}\le\sqrt{x\left(4x+1\right)}\)