Question

[cao thị quỳnh như]

tìm cặp số nguyên x,y

a x.y= 21

b (2x-1).(2y+1)= -35

Answer 1

[Nguyễn Lê Phước Thịnh]

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 \(y\in\left\{-18;-1;17;3;-3;-4;2\right\}\)

Answer 2

[Nguyễn Thị Thùy Trâm]

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}