tìm một số, biết:\(1\frac{2}{7}\)của nó bằng -18
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Đặt A \(=1+5+5^2+...+5^{2000}\)
Ta có: 5A\(=5+5^2+5^3+...+5^{2001}\)
5A-A\(=5^{2001}-1\)
4A\(=5^{2001}-1\)
A\(=\frac{5^{2001}-1}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : \(\left|x-22\right|\ge0\forall x\)
\(\left|y-12\right|\ge0\forall y\)
\(\Rightarrow\left|x-22\right|+\left|y-12\right|\ge0\forall x;y\)
Dấu \("="\)xảy ra \(\Leftrightarrow\hept{\begin{cases}\left|x-22\right|=0\\\left|y-12\right|=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x-22=0\\y-12=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=22\\y=12\end{cases}}\)
Vậy \(\hept{\begin{cases}x=22\\y=12\end{cases}}\)
Trường hợp :
\(\left|x-22\right|+\left|y-12\right|< 0\left(l\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Để \(-\frac{1}{n+2018}\in Z\)
\(\Leftrightarrow-1⋮n+2018\)
\(\Leftrightarrow n+2018\inƯ\left(-1\right);n+2018\in Z\)
\(\Leftrightarrow n+2018\in\left\{1;-1\right\}\)
\(\Leftrightarrow n\in\left\{-2017;-2019\right\}\)
Vậy \(n\in\left\{-2017;-2019\right\}\)
Chúc bạn học tốt !!!
![](https://rs.olm.vn/images/avt/0.png?1311)
a)\(=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}\)
\(=\left(\frac{-3}{7}+\frac{3}{7}\right)-\left(\frac{15}{26}+\frac{2}{13}\right)\)
\(=0-\frac{19}{26}\)
\(=-\frac{19}{26}\)
c)\(=\frac{-11}{23}.\left(\frac{6}{7}+\frac{8}{7}\right)-\frac{1}{23}\)
\(=\frac{-11}{23}.2-\frac{1}{23}\)
\(=\frac{-22}{23}-\frac{1}{23}\)
\(=-1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x+1}{99}+\frac{x+2}{98}+\frac{x+3}{97}+\frac{x+4}{96}=-4\)
\(\Rightarrow\left(\frac{x+1}{99}+1\right)+\left(\frac{x+2}{98}+1\right)+\left(\frac{x+3}{97}+1\right)+\left(\frac{x+4}{96}+1\right)=-4+4\)
\(\Rightarrow\frac{x+100}{99}+\frac{x+100}{98}+\frac{x+100}{97}+\frac{x+100}{96}=0\)
\(\Rightarrow\left(x+100\right).\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+\frac{1}{96}\right)=0\)
Mà \(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+\frac{1}{96}>0\)
\(\Rightarrow x+100=0\)
\(\Rightarrow x=0-100\)
\(\Rightarrow x=-100\)
Chúc bạn học tốt !!!!
\(\frac{x+1}{99}+\frac{x+2}{98}+\frac{x+3}{97}+\frac{x+4}{96}=-4\)
\(\Leftrightarrow\left(\frac{x+1}{99}+1\right)+\left(\frac{x+2}{98}+1\right)+\left(\frac{x+3}{97}+1\right)+\left(\frac{x+4}{96}+1\right)=0\)
\(\Leftrightarrow\frac{x+100}{99}+\frac{x+100}{98}+\frac{x+100}{97}+\frac{x+100}{96}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+\frac{1}{96}\right)=0\)
\(\Leftrightarrow x+100=0\)
\(\Leftrightarrow x=-100\)
Vậy...
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi \(d\in\left(2n+1;3n+2\right)\)
\(\Rightarrow\hept{\begin{cases}2n+1⋮d\\3n+2⋮d\end{cases}\Rightarrow\hept{\begin{cases}6n+3⋮d\\6n+4⋮d\end{cases}\Rightarrow1⋮}d\Rightarrow d=1}\)
\(\Rightarrowđpcm\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1\frac{2}{7}=\frac{9}{7}\)
Số đó là :
\(-18:\frac{9}{7}=-14\)
Vậy số đó là \(-14\)
Chúc bạn học tốt !!!!
ngu
1/2/7=9/7
9/7x(-18)
-23/1/7
con óc chó