Question

[Nguyễn Thị Kim Loan]

Tìm các cặp số nguyên x,y biết :

1. ( 2x + 1 ) . ( y - 3 ) = 12
2. x.y +  3x - 7y = 21
3. x.y - 3x - 2y = 11

Answer 1

[Trần Thùy Dung]

Vì \(\left(2x+1\right)\left(y-3\right)=12\)

\(\Rightarrow2x+1;y-3\inƯ\left(12\right)=\left\{-12;-6;-4;-3;-2;-1;1;2;3;4;6;12\right\}\)

Vì \(2x+1\) là số lẻ nên \(2x+1\in\left\{-3;-1;1;3\right\}\)

Ta có bảng sau:

2x+1	-3	-1	1	3
2x	-4	-2	0	2
x	-2	-1	0	1
y-3	-4	-12	12	4
y	-1	-9	15	7

Vậy \(\left(x;y\right)\in\left\{\left(-2;-1\right);\left(-1;-9\right);\left(0;15\right);\left(1;7\right)\right\}\)

Answer 2

[Trần Thùy Dung]

Ta có:

\(xy+3x-7y=21\)

\(\Rightarrow x.\left(y+3\right)-7y-21=21-21=0\)

\(x\left(y+3\right)-\left(21+7y\right)=0\)

\(x.\left(y+3\right)-7.\left(y+3\right)=0\)

\(\left(x-7\right)\left(y+3\right)=0\)

\(\Rightarrow x-7=0\) hoặc \(y+3=0\)

TH1: x-7=0

x=0+7=7

TH2:y+3=0

y=0-3=-3

Vậy x=7; y=-3