Question

Tìm cặp số nguyên x, y sao cho:

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

b, x.(y + 2) = 8

c, xy - 2x - 2y = 0

d, (x + 3).(y + 2) = 1

Answer 1

a: \(\Leftrightarrow\left(x-1;y+1\right)\in\left\{\left(1;5\right);\left(5;1\right);\left(-1;-5\right);\left(-5;-1\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(2;4\right);\left(6;0\right);\left(0;-6\right);\left(-4;-2\right)\right\}\)

b: \(\Leftrightarrow\left(x;y+2\right)\in\left\{\left(1;8\right);\left(2;4\right);\left(4;2\right);\left(8;1\right);\left(-1;-8\right);\left(-8;-1\right);\left(-2;-4\right);\left(-4;-2\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(1;6\right);\left(2;2\right);\left(4;0\right);\left(8;-1\right);\left(-1;-10\right);\left(-8;-3\right);\left(-2;-6\right);\left(-4;-4\right)\right\}\)

c: \(\Leftrightarrow y\left(x-2\right)-2x+4=4\)

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

\(\Leftrightarrow\left(x-2;y-2\right)\in\left\{\left(1;4\right);\left(4;1\right);\left(2;2\right);\left(-2;-2\right);\left(-4;-1\right);\left(-1;-4\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(3;6\right);\left(6;3\right);\left(4;4\right);\left(0;0\right);\left(-2;1\right);\left(1;-2\right)\right\}\)

d: \(\Leftrightarrow\left(x+3;y+2\right)\in\left\{\left(1;1\right);\left(-1;-1\right)\right\}\)

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