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1, xy+2x-2y-5=0
=> x.( y+2)-2.(y+2)=5
=> (y+2).(x-2)=5
Vì x, y thuộc Z => y+2; x-2 thuộc Z
Mà 5=1.5=-1.(-5) và hoán vị của chúng
Ta có bảng sau:
y+2 1 5 -1 -5
x-2 5 1 -5 -1
y -1 3 -3 -7
x 7 3 -3 1
nHỚ K CHO MIK NHÉ
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1) \(\left(x+1\right)\left(y+2\right)=-6\)
TH1 : \(\left[{}\begin{matrix}x+1=6\\y+2=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\y=-3\end{matrix}\right.\)
TH2 : \(\left[{}\begin{matrix}x+1=-6\\y+2=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-7\\y=-1\end{matrix}\right.\)
TH3 : \(\left[{}\begin{matrix}x+1=1\\y+2=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\y=-8\end{matrix}\right.\)
TH4 : \(\left[{}\begin{matrix}x+1=-1\\y+2=6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\y=4\end{matrix}\right.\)
TH5 : \(\left[{}\begin{matrix}x+1=2\\y+2=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\y=-5\end{matrix}\right.\)
TH6 : \(\left[{}\begin{matrix}x+1=-2\\y+2=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\y=1\end{matrix}\right.\)
TH7 : \(\left[{}\begin{matrix}x+1=3\\y+2=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\y=-4\end{matrix}\right.\)
TH8 : \(\left[{}\begin{matrix}x+1=-3\\y+2=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\y=0\end{matrix}\right.\)
Vây
Bạn có làm được câu mình tag bạn váo không? Võ Đông Anh Tuấn
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1) \(\left(x-1\right)\left(y-1\right)=5\)
\(\Leftrightarrow\left(x-1\right)\left(y-1\right)=1.5=5.1=\left(-1\right).\left(-5\right)=\left(-5\right).\left(-1\right)\)
Ta có bảng sau:
\(x-1\) | \(1\) | \(5\) | \(-1\) | \(-5\) |
\(y-1\) | \(5\) | \(1\) | \(-5\) | \(-1\) |
\(x\) | \(2\) | \(6\) | \(0\) | \(-4\) |
\(y\) | \(6\) | \(2\) | \(-4\) | \(0\) |
Vậy \(\left(x;y\right)=\left(2;6\right);\left(6;2\right);\left(0;-4\right);\left(-4;0\right)\)
2) \(x\left(y+2\right)=-8\)
\(\Leftrightarrow x\left(y+2\right)=2.\left(-4\right)=\left(-4\right).2=\left(-2\right).4=4.\left(-2\right)=1.\left(-8\right)=\left(-8\right).1=\left(-1\right).8=8.\left(-1\right)\)
Ta có bảng sau:
\(x\) | \(2\) | \(-4\) | \(-2\) | \(4\) | \(1\) | \(-8\) | \(-1\) | \(8\) |
\(y+2\) | \(-4\) | \(2\) | \(4\) | \(-2\) | \(-8\) | \(1\) | \(8\) | \(-1\) |
\(y\) | \(-6\) | \(0\) | \(2\) | \(-4\) | \(-10\) | \(-1\) | \(6\) | \(-3\) |
Vậy ...
![](https://rs.olm.vn/images/avt/0.png?1311)
1)\(y=\frac{x^2+3x+7}{x+3}=\frac{x\left(x+3\right)+7}{x+3}=x+\frac{7}{x+3}\)= > x +3 thuoc\(U_{\left(7\right)}=\left\{1;-1;7;-7\right\}\)
x thuoc \(\left\{-2;-4;3;-11\right\}\)
2)\(y=\frac{4x+3}{2x+6}=\frac{4x+12-8}{2x+6}=\frac{2\left(2x+6\right)-8}{2x+6}=2-\frac{8}{2x+6}\) =>2x+6 thuoc
\(U_{\left(8\right)}=\left\{1;-1;2;-2;4;-4;8;-8\right\}\)
=>x thuoc \(\left\{-2;-4;-1;-5;1;-7\right\}\)
4)\(y=\frac{4x+1}{3x-1}\)
\(3y=\frac{12x+3}{3x-1}=\frac{12x-4+7}{3x-1}=\frac{4\left(3x-1\right)+7}{3x-1}=4+\frac{7}{3x-1}\)
3x+1 thuoc {1;-1;7;-7}
3x thuoc {0;-2;6;-8}
x thuoc {0;2}
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