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\(D=\frac{2x+1}{x-3}=\frac{2x-6}{x-3}+\frac{7}{x-3}=2+\frac{7}{x-3}\in Z\Leftrightarrow x-3\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\)
\(\Leftrightarrow x\in\left\{-4;2;4;10\right\}\)
D= \(\frac{2x+1}{x-3}=2+\frac{7}{x-3}\)
để D dương thì x-3 là uocs của 7=(-1,1,-7,7)
xét từng TH:
x-3=-1=> x=2
x-3=1=>x=4
x-3=-7=>x=-4
x-3=7=>x=10
các giá trị x là 2,4,-4,10
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Tìm x biết:
a) 3x-|2x+1|=2
b)2.|5x-3|-2x=14
c)|x+1|+|x+2|+|x+3|=4x
d)|x-2|+|3-2x|=2x+1
e)|x-3|=(-2).|x+4|
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\(\left|2x-1\right|+\left|2x-3\right|=\left|2x-1\right|+\left|3-2x\right|\)
\(\Rightarrow A=\left|2x-1\right|+\left|3-2x\right|\ge\left|2x-1+3-2x\right|\)
\(\Rightarrow A=\left|2x-1\right|+\left|3-2x\right|\ge\left|2\right|=2\)
dấu "="xảy ra khi \(\left(2x-1\right).\left(3-2x\right)\ge0\)
\(\Rightarrow\frac{1}{2}\le x\le\frac{3}{2}\)
vậy min A=2 khi \(\frac{1}{2}\le x\le\frac{3}{2}\)
\(\left|x-3\right|=\left|2x+1\right|\)
\(x-3=2x+1\)
\(x-3-2x-1=0\)
\(-x-4=0\)
\(-x=4\)
\(x=-4\)
nhắc tớ sai đâu sửa nha !
Brainchild vs t thì you sai cả bài
Ta có | x - 3 | = | 2x + 1|
\(\Leftrightarrow\orbr{\begin{cases}x-3=2x+1\\x-3=-2x-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-2x=1+3\\x+2x=3-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}-x=4\\3x=2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-4\\x=\frac{2}{3}\end{cases}}\)
Vậy \(x\in\left\{-4;\frac{2}{3}\right\}\)
Học tốt
Takigawa Miraii_