Question

Tìm số nguyên x :

1) ( x - 1) . ( y + 1 ) = 5

2) x . ( y + 2 ) = -8

3) xy - 2x - 2y = 0

4) 2x - 5 chia hết cho x - 1

Answer 1

1) \(\left(x-1\right)\left(y-1\right)=5\)

\(\Leftrightarrow\left(x-1\right)\left(y-1\right)=1.5=5.1=\left(-1\right).\left(-5\right)=\left(-5\right).\left(-1\right)\)

Ta có bảng sau:

\(x-1\)	\(1\)	\(5\)	\(-1\)	\(-5\)
\(y-1\)	\(5\)	\(1\)	\(-5\)	\(-1\)
\(x\)	\(2\)	\(6\)	\(0\)	\(-4\)
\(y\)	\(6\)	\(2\)	\(-4\)	\(0\)

Vậy \(\left(x;y\right)=\left(2;6\right);\left(6;2\right);\left(0;-4\right);\left(-4;0\right)\)

2) \(x\left(y+2\right)=-8\)

\(\Leftrightarrow x\left(y+2\right)=2.\left(-4\right)=\left(-4\right).2=\left(-2\right).4=4.\left(-2\right)=1.\left(-8\right)=\left(-8\right).1=\left(-1\right).8=8.\left(-1\right)\)

Ta có bảng sau:

\(x\)	\(2\)	\(-4\)	\(-2\)	\(4\)	\(1\)	\(-8\)	\(-1\)	\(8\)
\(y+2\)	\(-4\)	\(2\)	\(4\)	\(-2\)	\(-8\)	\(1\)	\(8\)	\(-1\)
\(y\)	\(-6\)	\(0\)	\(2\)	\(-4\)	\(-10\)	\(-1\)	\(6\)	\(-3\)

Vậy ...