Question

Tìm các cặp số nguyên (x;y) thỏa mãn  y(x + 3) - 5x - 15 = 2

Answer 1

\(y\left(x+3\right)-5x-15=2\\ \Rightarrow y\left(x+3\right)-\left(5x+15\right)=2\\ \Rightarrow y\left(x+3\right)-5\left(x+3\right)=2\\ \Rightarrow\left(y-5\right)\left(x+3\right)=2\)

Vì \(x,y\in Z\Rightarrow\left\{{}\begin{matrix}y-5,x+3\in Z\\y-5,x+3\inƯ\left(2\right)\end{matrix}\right.\)

Ta có bảng:

x+3	1	2	-1	-2
y-5	2	1	-2	-1
x	-2	-1	-4	-5
y	7	6	3	4

Vậy \(\left(x,y\right)\in\left\{\left(-2;7\right);\left(-1;6\right);\left(-4;3\right);\left(-5;4\right)\right\}\)

 

Answer 2

=>y.(x+3)-5(x+3)=2

=>(y-5).(x+3)=2

x+3	1	-1	2	-2
y-5	1	-1	2	-2
x	-2	-1	-4	-5
y	7	6	3	4