Tìm số nguyên x,y, biết rằng a) (x-3).(y-5)=11 b)(x-1).(xy-5)=5

`a)`

`(x - 3)(y - 5) = 11`

`=> 11 = {(1 . 11),(11 . 1),((-1) . (-11)),((-11) . (-1)):}`

`TH_{1} :`

\(\left[ \begin{array}{l}x - 3 = 1\\y - 5 = 11\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 1 + 3\\x = 11 + 5\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 4\\x = 16\end{array} \right.\)

`TH_{2} :`

\(\left[ \begin{array}{l}x - 3 = 11\\x - 5 = 1\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 11 + 3\\x = 1 + 5\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 14\\x = 6\end{array} \right.\)

`TH_{3} :`

\(\left[ \begin{array}{l}x - 3 = -1\\y - 5 = -11\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = -1 + 3\\x = -11 + 5\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 2\\x = -6\end{array} \right.\)

`TH_{4} :`

\(\left[ \begin{array}{l}x - 3 = -11\\x - 5 = -1\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = -11 + 3\\x = -1 + 5\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = -8\\x = 4\end{array} \right.\)

Vậy: các cặp `xy` thỏa mãn là: `(4; 16) ; (14; 6) ; (2; -6) ; (-8;4)`

`b)`

`(x - 1)(xy - 5) = 5`

`=> 5 = {(1 . 5),(5 . 1),((-1) . (-5)),((-5) . (-1)):}`

`TH_{1} :`

\(\left[ \begin{array}{l}x - 1 = 1\\xy - 5 = 5\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 2\\y = 5\end{array} \right.\)

`TH_{2} :`

\(\left[ \begin{array}{l}x - 1 = 5\\xy - 5 = 1\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 6\\y = 1\end{array} \right.\)

`TH_{3} :`

\(\left[ \begin{array}{l}x - 1 = -1\\xy - 5 = -5\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 0\\y = 0\end{array} \right.\)

`TH_{4} :`

\(\left[ \begin{array}{l}x - 1 = -5\\xy - 5 = -1\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = -4\\y = -1\end{array} \right.\)

Vậy: các cặp `xy` thỏa mãn là: `(2; 5) ; (6; 1) ; (0; 0) ; (-4; -1)`