Tìm x, y thuộc ℤ biết 3xy - 2x + 5y = 29
Tìm x, y ∈ ℤ biết 3xy – 2x + 5y = 29
3xy − 2x + 5y = 29
9xy − 6x + 15y = 87
(9xy − 6x) + (15y − 10) = 77
3x(3y − 2) + 5(3y−2) = 77
(3y − 2)(3x + 5) = 77
⇒ (3y − 2) và (3x + 5) là Ư(77) = {±1, ±7, ±11, ±77}
Ta có bảng giá trị sau:
|
3x + 5 |
–77 |
–11 |
–7 |
–1 |
1 |
7 |
11 |
77 |
|
3y – 2 |
–1 |
–7 |
–11 |
–77 |
77 |
11 |
7 |
1 |
|
x |
\(\frac{{ - 82}}{3}\) |
\(\frac{{ - 16}}{3}\) |
–4 |
–2 |
\(\frac{{ - 4}}{3}\) |
\(\frac{2}{3}\) |
2 |
24 |
|
y |
\(\frac{1}{3}\) |
\(\frac{{ - 5}}{3}\) |
–3 |
–25 |
\(\frac{{79}}{3}\) |
\(\frac{{13}}{3}\) |
3 |
1 |
Do x, y ∈ ℤ nên (x,y) ∈ {(−4; −3), (−2; −25), (2; 3), (24; 1)}
Vậy (x,y) ∈ {(−4; −3); (−2; −25); (2; 3); (24; 1)}.