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1. \(\Leftrightarrow\left(2x-1\right)\left(3x+1\right)< 0\)
\(\Rightarrow-\frac{1}{3}< x< \frac{1}{2}\)
2. \(\Leftrightarrow\left(x-2\right)\left(3-2x\right)>0\)
\(\Rightarrow\frac{3}{2}< x< 2\)
3. \(\Leftrightarrow\left(5x-3\right)^2>0\)
\(\Rightarrow x\ne\frac{3}{5}\)
4. \(\Leftrightarrow-3\left(x-\frac{1}{6}\right)-\frac{59}{12}< 0\)
\(\Rightarrow x\in R\)
5. \(\Leftrightarrow2\left(x-1\right)^2+5\ge0\)
\(\Rightarrow x\in R\)
6. \(\Leftrightarrow\left(x+2\right)\left(8x+7\right)\le0\)
\(\Rightarrow-2\le x\le-\frac{7}{8}\)
7.
\(\Leftrightarrow\left(x-1\right)^2+2>0\)
\(\Rightarrow x\in R\)
8. \(\Leftrightarrow\left(3x-2\right)\left(2x+1\right)\ge0\)
\(\Rightarrow\left[{}\begin{matrix}x\le-\frac{1}{2}\\x\ge\frac{2}{3}\end{matrix}\right.\)
9. \(\Leftrightarrow\frac{1}{3}\left(x+3\right)\left(x+6\right)< 0\)
\(\Rightarrow-6< x< -3\)
10. \(\Leftrightarrow x^2-6x+9>0\)
\(\Leftrightarrow\left(x-3\right)^2>0\)
\(\Rightarrow x\ne3\)
c: \(\Leftrightarrow\left\{{}\begin{matrix}4x+3>=0\\\left(x+2-4x-3\right)\left(x+2+4x+3\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{3}{4}\\\left(-3x-1\right)\left(5x+5\right)< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{3}{4}\\\left(3x+1\right)\left(x+1\right)>0\end{matrix}\right.\)
\(\Leftrightarrow x>-\dfrac{1}{3}\)
d: \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x-2< 0\\2x+1>=0\end{matrix}\right.\\\left\{{}\begin{matrix}3x-2>=0\\\left(2x+1-3x+2\right)\left(2x+1+3x-2\right)>=0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< \dfrac{2}{3}\\x>-\dfrac{1}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x>=\dfrac{2}{3}\\\left(-x+3\right)\left(5x-1\right)>=0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-\dfrac{1}{2}< x< \dfrac{2}{3}\\\left\{{}\begin{matrix}x>=\dfrac{2}{3}\\\left(x-3\right)\left(5x-1\right)< =0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{-1}{2}< x< \dfrac{2}{3}\\\dfrac{2}{3}< =x< =3\end{matrix}\right.\)
a/ - Với \(x>\frac{1}{4}\) PT vô nghiêm
- Với \(x\le\frac{1}{4}\)
\(\Leftrightarrow\left(x^2-1\right)^2=\left(1-4x\right)^2\)
\(\Leftrightarrow\left(x^2+4x-2\right)\left(x^2-4x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x^2+4x-2=0\\x^2-4x=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-2+\sqrt{6}\left(l\right)\\x=-2-\sqrt{6}\\x=4\left(l\right)\\x=0\end{matrix}\right.\)
2.
- Với \(x\ge-\frac{1}{4}\Leftrightarrow4x+1=x^2+2x-4\)
\(\Leftrightarrow x^2-2x-5=0\Rightarrow\left[{}\begin{matrix}x=1+\sqrt{6}\\x=1-\sqrt{6}\left(l\right)\end{matrix}\right.\)
- Với \(x< -\frac{1}{4}\)
\(\Leftrightarrow-4x-1=x^2+2x-4\)
\(\Leftrightarrow x^2+6x-3=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-3+2\sqrt{3}\left(l\right)\\x=-3-2\sqrt{3}\end{matrix}\right.\)
3.
- Với \(x\ge\frac{5}{3}\)
\(\Leftrightarrow3x-5=2x^2+x-3\)
\(\Leftrightarrow2x^2-2x+2=0\left(vn\right)\)
- Với \(x< \frac{5}{3}\)
\(\Leftrightarrow5-3x=2x^2+x-3\)
\(\Leftrightarrow2x^2+4x-8=0\Rightarrow\left[{}\begin{matrix}x=-1+\sqrt{5}\\x=-1-\sqrt{5}\end{matrix}\right.\)
4. Do hai vế của pt đều không âm, bình phương 2 vế:
\(\Leftrightarrow\left(x^2-2x+8\right)^2=\left(x^2-1\right)^2\)
\(\Leftrightarrow\left(x^2-2x+8\right)^2-\left(x^2-1\right)^2=0\)
\(\Leftrightarrow\left(2x^2-2x+7\right)\left(-2x+9\right)=0\)
\(\Leftrightarrow-2x+9=0\Rightarrow x=\frac{9}{2}\)
1/
\(\Leftrightarrow2\left(x^2-5x+6\right)\left(x-4\right)>0\)
\(\Leftrightarrow2\left(x-2\right)\left(x-3\right)\left(x-4\right)>0\)
\(\Rightarrow\left[{}\begin{matrix}x>4\\2< x< 3\end{matrix}\right.\)
2/ Không dịch được đề
bài 1 đề mình là bé hơn 0 mà bạn :))))))
dù sao cug cam on nhé
1) \(-5x+10\ge0\Leftrightarrow-5x\ge-10\Leftrightarrow x\le2\)
Tìm x biết:
b/\(\left(2x+3\right)^2-\left(5x-4\right)\left(5x+4\right)=\left(x+5\right)^2-\left(3x-1\right)\left(7x+2\right)-\left(x^2-x+1\right)\)
<=> \(4x^2 +12x+9-25x^2+16-x^2-10x-25+21x^2+6x-7x-2+x^2-x+1=0\)
<=>0x-1=0
<=>0x=1 (vô lí) (dòng này không cần ghi thêm cũng được)
=> Không có giá trị x nào thỏa mãn
c/ \((1-3x)^2-(x-2)(9x+1)=(3x-4)(3x+4)-9(x+3)^2\)
<=>\(1-6x+9x^2-9x^2-x+18x+2-9x^2+16+9x^2+54x+81=0\)
<=> 65x+100=0
<=> x=\(\dfrac{-20}{13}\)
d/\((3x+4)(3x-4)-(2x+5)^2=(x-5)^2+(2x+1)^2-(x^2-2x)+(x-1)^2\)
<=> \(9x^2-16-4x^2-20x-25-x^2+10x-25-4x^2-4x-1+x^2+2x-x^2+2x-1=0\)
<=> -10x-68=0
<=> x=\(\dfrac{-34}{5}\)
Câu 1:
- Với \(x< 1\Rightarrow\left\{{}\begin{matrix}VT\ge0\\VP< 0\end{matrix}\right.\) BPT vô nghiệm
- Với \(x\ge1\) hai vế ko âm, bình phương:
\(\left(-2x^2+4x-1\right)^2< \left(x-1\right)^2\)
\(\Leftrightarrow\left(x-1\right)^2-\left(-2x^2+4x-1\right)^2>0\)
\(\Leftrightarrow\left(2x^2-3x\right)\left(-2x^2+5x-2\right)>0\)
\(\Rightarrow\left[{}\begin{matrix}0< x< \frac{1}{2}\\\frac{3}{2}< x< 2\end{matrix}\right.\) \(\Rightarrow\frac{3}{2}< x< 2\)
Câu 2:
- Với \(1\le x\le2\Leftrightarrow-x^2+3x-2\ge2x-x^2\)
\(\Leftrightarrow x\ge2\Rightarrow x=2\)
- Với \(\left[{}\begin{matrix}x< 1\\x>2\end{matrix}\right.\) \(\Leftrightarrow x^2-3x+2\ge2x-x^2\)
\(\Leftrightarrow2x^2-5x+2\ge0\Rightarrow\left[{}\begin{matrix}x\le\frac{1}{2}\\x\ge2\end{matrix}\right.\)
Kết hợp lại ta được nghiệm của BPT: \(\left[{}\begin{matrix}x\le\frac{1}{2}\\x\ge2\end{matrix}\right.\)