Question

Tìm các số nguyên x, y sao cho: (x - 3).(y + 2) = -5.

Answer 1

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

\(\Rightarrow x-3;y+2\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

\(\Rightarrow\)Ta có bảng giá trị

\(x-3\)	\(1\)	\(-1\)	\(5\)	\(-5\)
\(y+2\)	\(-5\)	\(5\)	\(-1\)	\(1\)
\(x\)	\(4\)	\(2\)	\(8\)	\(-2\)
\(y\)	\(-7\)	\(3\)	\(-3\)	\(-1\)

Vậy \(\left(x;y\right)\in\left\{\left(4;-7\right);\left(2;3\right);\left(8;-3\right);\left(-2;-1\right)\right\}\)

Answer 2

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

\(\Rightarrow\left(x-3\right)\left(y+2\right)=-1.5=5.\left(-1\right)=-5.1=1.\left(-5\right)\)

Ta có bảng sau :

\(x-3\)	\(-1\)	\(5\)	\(-5\)	\(1\)
\(y+2\)	\(5\)	\(-1\)	\(1\)	\(-5\)
\(x\)	\(2\)	\(8\)	\(-2\)	\(4\)
\(y\)	\(3\)	\(-3\)	\(-1\)	\(-7\)

Vậy \(x,y\in\left\{\left(2,3\right);\left(8,-3\right);\left(-2,-1\right);\left(4,-7\right)\right\}\)

Answer 3

Ta có \(\left(x-3\right)\left(y+2\right)=5=\left(-1\right)5=\left(-5\right)1\)

x-3	-1	5	1	-5
y+2	5	-1	-5	1
x	2	8	4	-2
y	3	-3	-7	-1

Vậy các cặp số nguyên x,y thỏa mãn là (2;3);(8;-3);(4;-7);(-2;-1)