Question

[Trang]

Tìm các cặp số nguyên x,y thỏa mãn:

a, xy-x-y=1

b, xy-2x-2y=1

c,y²  = x² -4x+15

Answer 1

[Phùng Minh Quân]

\(a)\)\(xy-x-y=1\)

\(\Leftrightarrow\)\(\left(xy-x\right)-\left(y-1\right)=2\)

\(\Leftrightarrow\)\(x\left(y-1\right)-\left(y-1\right)=2\)

\(\Leftrightarrow\)\(\left(x-1\right)\left(y-1\right)=2\)

\(\Rightarrow\)\(\left(x-1\right);\left(y-1\right)\inƯ\left(2\right)\)

Lập bảng : 

\(x-1\)	\(1\)	\(2\)	\(-1\)	\(-2\)
\(y-1\)	\(2\)	\(1\)	\(-2\)	\(-1\)
\(x\)	\(2\)	\(3\)	\(0\)	\(-1\)
\(y\)	\(3\)	\(2\)	\(-1\)	\(0\)

Vậy \(\left(x,y\right)\in\left\{\left(2;3\right),\left(3;2\right),\left(0;-1\right),\left(-1;0\right)\right\}\)
Chúc bạn học tốt ~ 

Answer 2

[Phùng Minh Quân]

\(b)\)\(xy-2x-2y=1\)

\(\Leftrightarrow\)\(\left(xy-2x\right)-\left(2y-4\right)=5\)

\(\Leftrightarrow\)\(x\left(y-2\right)-2\left(y-2\right)=5\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(y-2\right)=5\)

\(\Rightarrow\)\(\left(x-2\right);\left(y-2\right)\inƯ\left(5\right)\)

Lập bảng : 

\(x-2\)	\(1\)	\(5\)	\(-1\)	\(-5\)
\(y-2\)	\(5\)	\(1\)	\(-5\)	\(-1\)
\(x\)	\(3\)	\(7\)	\(1\)	\(-3\)
\(y\)	\(7\)	\(3\)	\(-3\)	\(1\)

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

Chúc bạn học tốt ~