a) Ta có: xy=21
\(\Rightarrow x,y\inƯ\left(21\right)\)
\(\Rightarrow x,y\in\left\{1;3;7;21;-1;-3;-7;-21\right\}\)
*Trường hợp 1: \(\left\{{}\begin{matrix}x=1\\y=21\end{matrix}\right.\)
*Trường hợp 2: \(\left\{{}\begin{matrix}x=21\\y=1\end{matrix}\right.\)
*Trường hợp 3: \(\left\{{}\begin{matrix}x=3\\y=7\end{matrix}\right.\)
*Trường hợp 4: \(\left\{{}\begin{matrix}x=7\\y=3\end{matrix}\right.\)
*Trường hợp 5: \(\left\{{}\begin{matrix}x=-1\\y=-21\end{matrix}\right.\)
*Trường hợp 6: \(\left\{{}\begin{matrix}x=-21\\y=-1\end{matrix}\right.\)
*Trường hợp 7: \(\left\{{}\begin{matrix}x=-3\\y=-7\end{matrix}\right.\)
*Trường hợp 8: \(\left\{{}\begin{matrix}x=-7\\y=-3\end{matrix}\right.\)
Vậy: \(x\in\left\{1;3;7;21;-1;-3;-7;-21\right\}\) và \(y\in\left\{1;3;7;21;-1;-3;-7;-21\right\}\)
b) Ta có: (2x-1)(2y+1)=-35
\(\Rightarrow2x-1;2y+1\inƯ\left(-35\right)\)
\(\Rightarrow2x-1;2y+1\in\left\{1;5;7;35;-1;-5;-7;-35\right\}\)
*Trường hợp 1:
\(\left\{{}\begin{matrix}2x-1=1\\2y+1=-35\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=2\\2y=-36\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-18\end{matrix}\right.\)(tm)
*Trường hợp 2:
\(\left\{{}\begin{matrix}2x-1=-35\\2y+1=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-34\\2y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-17\\y=-1\end{matrix}\right.\)(tm)
*Trường hợp 3:
\(\left\{{}\begin{matrix}2x-1=-1\\2y+1=35\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=0\\2y=34\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=17\end{matrix}\right.\)(tm)
*Trường hợp 4:
\(\left\{{}\begin{matrix}2x-1=35\\2y+1=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=36\\2y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=18\\y=-1\end{matrix}\right.\)(tm)
*Trường hợp 5:
\(\left\{{}\begin{matrix}2x-1=-5\\2y+1=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-4\\2y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=3\end{matrix}\right.\)(tm)
*Trường hợp 6:
\(\left\{{}\begin{matrix}2x-1=7\\2y+1=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=8\\2y=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=-3\end{matrix}\right.\)(tm)
*Trường hợp 7:
\(\left\{{}\begin{matrix}2x-1=5\\2y+1=-7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=6\\2y=-8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-4\end{matrix}\right.\)(tm)
*Trường hợp 8:
\(\left\{{}\begin{matrix}2x-1=-7\\2y+1=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-6\\2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=2\end{matrix}\right.\)
Vậy: \(x\in\left\{1;-17;0;18;-2;4;3;-3\right\}\) và \(y\in\left\{-18;-1;17;3;-3;-4;2\right\}\)
a) x . y = 21
Nên 21 ⋮ x
Vậy x ∈ Ư(21) = {-1; 1; -3; 3; -7; 7; -21; 21}
Ta có bảng sau :
| x | -1 | 1 | -3 | 3 | -7 | 7 | -21 | 21 |
| y | -21 | 21 | -7 | 7 | -3 | 3 | -1 | 1 |
➤ {x ; y} = {-1 ; -21}
{x ; y} = {1 ; 21}
{x ; y} = {-3 ; -7}
{x ; y} = {3 ; 7}
{x ; y} = {-7 ; -3}
{x ; y} = {7 ; 3}
{x ; y} = {-21 ; -1}
{x ; y} = {21 ; 1}
b) (2x - 1) . (2y + 1) = -35
Nên -35 ⋮ 2x - 1
Vậy 2x - 1 ∈ Ư(-35) = {-1; 1; -5; 5; -7; 7; -35; 35}
Ta có bảng sau :
| 2x - 1 | -1 | 1 | -5 | 5 | -7 | 7 | -35 | 35 |
| 2x | 0 | 2 | -4 | 6 | -6 | 8 | -34 | 36 |
| x | 0 | 1 | -2 | 3 | -3 | 4 | -17 | 18 |
| 2y + 1 | 35 | -35 | 7 | -7 | 5 | -5 | 1 | -1 |
| 2y | 34 | -36 | 6 | -8 | 4 | -6 | 0 | -2 |
| y | 17 | -18 | 3 | -4 | 2 | -3 | 0 | -1 |
➤ {x ; y} = {0 ; 17}
{x ; y} = {1 ; -18}
{x ; y} = {-2 ; 3}
{x ; y} = {3 ; -4}
{x ; y} = {-3 ; 2}
{x ; y} = {4 ; -3}
{x ; y} = {-17 ; 0}
{x ; y} = {18 ; -1}
