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Ta có: \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+2003\right)=4+1007\cdot2003\)
\(\Leftrightarrow2004x+\dfrac{2003\cdot2004}{2}=4+1007\cdot2003\)
\(\Leftrightarrow2004x=10019\)
hay \(x=\dfrac{10019}{2004}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
xy + 2x - 3y = 9
\(\Leftrightarrow\) 2x + xy - 3y - 6 = 3
\(\Leftrightarrow\) x(2 + y) - 3(y + 2) = 3
\(\Leftrightarrow\) (2 + y)(x - 3) = 3
Vì x, y \(\in\) Z nên (2 + y)(x - 3) \(\in\) Z. Ta có bảng sau:
x - 3 | 3 | 1 | -1 | -3 |
2 + y | 1 | 3 | -3 | -1 |
x | 6(TM) | 4(TM) | 2(TM) | 0(TM) |
y | -1(TM) | 1(TM) | -5(TM) | -3(TM) |
Vậy phương trình có nghiệm (x; y) = {(6; 1); (4; 1); (2; -5); (0; -3)}
Chúc bn học tốt!
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow x+3\in\left\{1;-1;3;-3;9;-9\right\}\)
hay \(x\in\left\{-2;-4;0;-6;6;-12\right\}\)
\(\dfrac{x-6}{x+3}=\dfrac{x+3-6}{x+3}=\dfrac{x+3}{x+3}-\dfrac{6}{x+3}=1-\dfrac{6}{x+3}\)
\(\dfrac{x-6}{x+3}⋮x+3\Rightarrow\dfrac{6}{x+3}⋮x+3\\ \Rightarrow x+3\inƯ_{\left(6\right)}=\left\{-6;-3;-2;-1;1;2;3;6\right\}\)
\(\Rightarrow x\in\left\{-9;-6;-5;-4;-2;-1;0;3\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(\dfrac{x+1}{2018}+\dfrac{x+1}{2019}+\dfrac{x+1}{2020}+\dfrac{x+1}{2021}=0\)
\(\Leftrightarrow x+1=0\)
hay x=-1
Ta có: \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+2013\right)=4+1007\cdot2013\)
\(\Leftrightarrow2014x+2027091=2027095\)
\(\Leftrightarrow2014x=4\)
hay \(x=\dfrac{2}{1007}\)
thanks bạn nha