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b: \(\Leftrightarrow\left(x-3;y+2\right)\in\left\{\left(1;11\right);\left(11;1\right);\left(-1;-11\right);\left(-11;-1\right)\right\}\)
hay \(\left(x,y\right)\in\left\{\left(4;9\right);\left(14;-1\right);\left(2;-13\right);\left(-8;-3\right)\right\}\)
c: \(\Leftrightarrow x\left(y-3\right)-y+3=3\)
=>(y-3)(x-1)=3
\(\Leftrightarrow\left(x-1;y-3\right)\in\left\{\left(1;3\right);\left(3;1\right);\left(-1;-3\right);\left(-3;-1\right)\right\}\)
hay \(\left(x,y\right)\in\left\{\left(2;6\right);\left(4;4\right);\left(0;0\right);\left(-2;2\right)\right\}\)
a) (2x+1)(2y-3)=36
=> 2x+1 ; 2y-3 thuộc Ư(36)={-1,-2,-3,-4,-6,-9,-13,-18,-36,1,2,3,4,6,9,13,18,36}
Ta có bảng :
| 2x+1 | -1 | -2 | -3 | -4 | -6 | -9 | -13 | -18 | -36 | 1 | 2 | 3 | 4 | 6 | 9 | 13 | 18 | 36 |
| 2y-3 | -36 | -18 | -13 | -9 | -6 | -4 | -3 | -2 | -1 | 36 | 18 | 13 | 9 | 6 | 4 | 3 | 2 | 1 |
| x | -1 | -3/2 | -2 | -5/2 | -7/2 | -5 | -7 | -19/2 | -37/2 | 0 | 1/2 | 1 | 3/2 | 5/2 | 4 | 6 | 17/2 | 35/2 |
| y | -33/2 | -15/3 | -5 | -3 | -3/2 | -1/2 | 0 | 1/2 | 1 | 39/2 | 21/2 | 8 | 6 | 9/2 | 7/2 | 3 | 5/2 | 2 |
Vậy ta có các cặp x,y thõa mãn đề bài là : (-2,-5);(-7,0);(1,8);(6,3)
a) \(xy+3x-2y=11\)
\(\Leftrightarrow x\left(y+3\right)-2y-6=5\)
\(\Leftrightarrow x\left(y+3\right)-2\left(y+3\right)=5\)
\(\Leftrightarrow\left(y+3\right)\left(x-2\right)=5\)
Lập bảng mà tìm
b) \(x+y=xy\)
\(\Leftrightarrow x+y-xy=0\)
\(\Leftrightarrow x+y\left(x-1\right)=0\)
\(\Leftrightarrow x-1+y\left(x-1\right)=-1\)
\(\Leftrightarrow\left(x-1\right)\left(1+y\right)=-1\)
Tìm nốt
a, xy+3x-7y=21
=>xy+3x-7y-21=0
=>x(y+3)-7(y+3)=0
=>(x-7)(y+3)=0
=>x=7,y=-3
b,xy+3x-2y=11
=>x(y+3)-2(y+3)=5
=>(x-2)(y+3)=5
=>x-2,y+3 thuộc ước của 5 cứ thế mà làm
CHÚC BẠN HỌC TỐT
\(a)xy+3x-7y=21\)
\(\Leftrightarrow xy+3x-7y-21=0\)
\(\Leftrightarrow\left(xy+3x\right)-\left(7y+21\right)=0\)
\(\Leftrightarrow x\left(y+3\right)-7\left(y+3\right)=0\)
\(\Leftrightarrow\left(y+3\right)\left(x-7\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}y+3=0\\x-7=0\end{cases}\Leftrightarrow\orbr{\begin{cases}y=-3\\x=7\end{cases}}}\)
\(b)xy+3x-2y=11\)
\(\Leftrightarrow\left(xy+3x\right)-2y=6+5\)
\(\Leftrightarrow x\left(y+3\right)-2y-6=5\)
\(\Leftrightarrow x\left(y+3\right)-\left(2y+6\right)=5\)
\(\Leftrightarrow x\left(y+3\right)-2\left(y+3\right)=5\)
\(\Leftrightarrow\left(y+3\right)\left(x-2\right)=5\Rightarrow\left(y+3\right);\left(x-2\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)
Xét các trường hợp :
- \(\hept{\begin{cases}y+3=5\\x-2=1\end{cases}\Leftrightarrow\hept{\begin{cases}y=2\\x=3\end{cases}}}\)
- \(\hept{\begin{cases}y+3=1\\x-2=5\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-2\\x=7\end{cases}}\)
- \(\hept{\begin{cases}y+3=-5\\x-2=-1\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-8\\x=1\end{cases}}\)
- \(\hept{\begin{cases}y+3=-1\\x-2=-5\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-4\\x=-3\end{cases}}\)
a: \(\Leftrightarrow6x+10⋮2x+1\)
\(\Leftrightarrow6x+3+7⋮2x+1\)
\(\Leftrightarrow2x+1\in\left\{1;-1;7;-7\right\}\)
hay \(x\in\left\{0;-2;3;-4\right\}\)
b: \(\Leftrightarrow6x+2⋮2x-1\)
\(\Leftrightarrow6x-3+5⋮2x-1\)
\(\Leftrightarrow2x-1\in\left\{1;-1;5;-5\right\}\)
hay \(x\in\left\{1;0;3;-2\right\}\)