a) \(\left(x-2\right)\left(y-3\right)=14\\ \left(x-2\right)\left(y-3\right)=1\cdot14=14\cdot1=2\cdot7=7\cdot2=\left(-1\right)\left(-14\right)=\left(-14\right)\left(-1\right)=\left(-2\right)\left(-7\right)=\left(-7\right)\left(-2\right)\)
Ta có bảng sau:
| x-2 | 1 | 14 | 2 | 7 | -1 | -14 | -2 | -7 |
| x | 3 | 16 | 4 | 9 | 1 | -12 | 0 | -5 |
| y-3 | 14 | 1 | 7 | 2 | -14 | -1 | -7 | -2 |
| y | 17 | 4 | 10 | 5 | -11 | 2 | -4 | 1 |
Vậy \(\left(x;y\right)\in\left\{\left(3;17\right);\left(16;4\right);\left(4;10\right);\left(9;5\right);\left(1;-11\right);\left(-12;2\right);\left(0;-4\right);\left(-5;1\right)\right\}\)
b) \(\left(x-5\right)\left(y+5\right)=21\\ \left(x-5\right)\left(y+5\right)=1\cdot21=21\cdot1=3\cdot7=7\cdot3=\left(-1\right)\left(-21\right)=\left(-21\right)\left(-1\right)=\left(-3\right)\left(-7\right)=\left(-7\right)\left(-3\right)\)
Ta có bảng sau:
| x-5 | 1 | 21 | 3 | 7 | -1 | -21 | -3 | -7 |
| x | 6 | 26 | 8 | 12 | 4 | -16 | 2 | -2 |
| y+5 | 21 | 1 | 7 | 3 | -21 | -1 | -7 | -3 |
| y | 16 | -4 | 2 | -2 | -26 | -6 | -12 | -8 |
Vậy \(\left(x;y\right)\in\left\{\left(6;16\right);\left(26;-4\right);\left(8;2\right);\left(12;-2\right);\left(4;-26\right);\left(-16;-6\right);\left(2;-12\right);\left(-2;-8\right)\right\}\)
c) \(x\left(y-1\right)-6\left(y-1\right)=25\\ \left(x-6\right)\left(y-1\right)=25\\ \left(x-6\right)\left(y-1\right)=1\cdot25=25\cdot1=5\cdot5=\left(-1\right)\left(-25\right)=\left(-25\right)\left(-1\right)=\left(-5\right)\left(-5\right)\)
Ta có bảng sau:
| x-6 | 1 | 25 | 5 | -1 | -25 | -5 |
| x | 7 | 31 | 11 | 5 | -19 | 1 |
| y-1 | 25 | 1 | 5 | -25 | -1 | -5 |
| y | 26 | 2 | 6 | -24 | 0 | -4 |
Vậy \(\left(x;y\right)\in\left\{\left(7;26\right);\left(31;2\right);\left(11;6\right);\left(5;-24\right);\left(-19;0\right);\left(1;-4\right)\right\}\)