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b) \(\left(5x-1\right)\left(2x-\frac{1}{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x-1=0\\2x-\frac{1}{3}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=1\\2x=\frac{1}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{5}\\x=\frac{1}{6}\end{matrix}\right.\)
e, \(-\frac{3}{4}-\left|\frac{4}{5}-x\right|=-1\)
\(\Leftrightarrow\left|\frac{4}{5}-x\right|=-\frac{3}{4}-\left(-1\right)\)
\(\Leftrightarrow\left|\frac{4}{5}-x\right|=\frac{1}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}\frac{4}{5}-x=\frac{1}{4}\\\frac{4}{5}-x=-\frac{1}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{7}{15}\\x=1,05\end{matrix}\right.\)
Vậy ....
\(\left(5x-1\right).\left(2x-\frac{1}{3}\right)=0\)
\(\Rightarrow5x-1=0\text{ hoặc }2x-\frac{1}{3}=0\)
\(\Rightarrow5x=1\text{ hoặc }2x=\frac{1}{3}\)
\(\Rightarrow x=\frac{1}{5}\text{ hoặc }x=\frac{1}{6}\)
\(\left(5x-1\right)\left(2x-\frac{1}{3}\right)=0\)
\(\Rightarrow\left[\begin{matrix}5x-1=0\\2x-\frac{1}{3}=0\end{matrix}\right.\Rightarrow\left[\begin{matrix}5x=1\\2x=\frac{1}{3}\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=\frac{1}{5}\\x=\frac{1}{6}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{1}{5};\frac{1}{6}\right\}\)
|5x-3| - 3x = 7
*Nếu \(x\ge\frac{3}{5}\)
5x - 3 - 3x = 7
2x = 10
x = 5 ( tm)
*Nếu \(x< \frac{3}{5}\)
3 - 5x - 3x = 7
-8x = 4
x = \(-\frac{1}{2}\)( tm )
Làm hơi khó nhìn , thông cảm. Mệt rùi :)
|x - 3| + |x - 5| - 4x = -28
*Nếu x < 3
3 - x + 5 - x - 4x = -28
-6x = -36
x = 6 ( loại do ko tm khoảng đang xét )
* nếu 3 < x < 5
x - 3 + 5 - x - 4x = -28
-4x = -30
x= \(\frac{15}{2}\) ( loại do ko tm khaongr đang xét )
*Nếu x > 5
x - 3 + x - 5 - 4x = -28
-2x = -20
x = 10 ( tm)
Vậy x =10
\(5x\left(2x-\frac{1}{2}\right)+2\left(2x-\frac{1}{2}\right)=0\)
\(\Rightarrow\left(2x-\frac{1}{2}\right)\left(5x+2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-\frac{1}{2}=0\\5x+2=0\end{cases}\Rightarrow}\orbr{\begin{cases}2x=\frac{1}{2}\\5x=-2\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{1}{4}\\x=\frac{-2}{5}\end{cases}}\)
5x.(2x - 1/2) + 2.(2x - 1/2) = 0
<=> 5x.2x + 5x.(-1/2) + 2.2x + 2.(-1/2) = 0
<=> 10x2 - 5/2x + 4x - 1 = 0
<=> 10x2 - 13/2x - 1 = 0
=> x = 1/4 hoặc x = -2/5
Bài 1:
\(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{6}\right|+...+\left|x+\frac{1}{101}\right|=101x\)
Ta thấy:
\(VT\ge0\Rightarrow VP\ge0\Rightarrow101x\ge0\Rightarrow x\ge0\)
\(\Rightarrow\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{6}\right)+...+\left(x+\frac{1}{101}\right)=101x\)
\(\Rightarrow\left(x+x+...+x\right)+\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{101}\right)=0\)
\(\Rightarrow10x+\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{10.11}\right)=0\)
\(\Rightarrow10x+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\right)=0\)
\(\Rightarrow10x+\left(1-\frac{1}{11}\right)=0\)
\(\Rightarrow10x+\frac{10}{11}=0\)
\(\Rightarrow10x=-\frac{10}{11}\Rightarrow x=-\frac{1}{11}\)(loại,vì x\(\ge\)0)
Bài 2:
Ta thấy: \(\begin{cases}\left(2x+1\right)^{2008}\ge0\\\left(y-\frac{2}{5}\right)^{2008}\ge0\\\left|x+y+z\right|\ge0\end{cases}\)
\(\Rightarrow\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|\ge0\)
Mà \(\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|=0\)
\(\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|=0\)
\(\Rightarrow\begin{cases}\left(2x+1\right)^{2008}=0\\\left(y-\frac{2}{5}\right)^{2008}=0\\\left|x+y+z\right|=0\end{cases}\)\(\Rightarrow\begin{cases}2x+1=0\\y-\frac{2}{5}=0\\x+y+z=0\end{cases}\)
\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\x+y+z=0\end{cases}\)\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\-\frac{1}{2}+\frac{2}{5}+z=0\end{cases}\)
\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\-\frac{1}{10}=-z\end{cases}\)\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\z=\frac{1}{10}\end{cases}\)
<==> ( 5x - 1)=0 < ===> 5x=1 <===>x=\(\frac{1}{5}\)
hoặc <===> (2x+\(\frac{1}{3}\)) =0 <===> 2x = \(\frac{-1}{3}\) <===> x =\(\frac{-1}{6}\)
vậy x = \(\frac{1}{5}\) hoặc x=\(\frac{-1}{6}\) nha bn !!!
bài này dễ ợt ah !!! cho mik đi :)))
\(\left(5x-1\right)\left(2x+\frac{1}{3}\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}5x-1=0\\2x+\frac{1}{3}=0\end{cases}\Leftrightarrow\hept{\begin{cases}5x=1\\2x=\frac{-1}{3}\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{1}{5}\\x=\frac{-1}{6}\end{cases}}}\)
\(\text{Vậy x }\varepsilon\left(\frac{1}{5};\frac{-1}{6}\right)\)