Tìm các cặp số nguyên x, y biết xy + 7x – 3y – 26  0

Lời giải:

xy + 7x – 3y – 26 = 0

suy ra y(x – 3) + 7(x – 3) – 5 = 0

(y + 7)(x – 3) = 5

(x – 3) và (y + 7) Î Ư(5) = {±1; ±5}

TH1: \(\left\{ \begin{array}{l}y + 7 = 1\\x - 3 = 5\end{array} \right.\,\,n\^e n\,\,\left\{ \begin{array}{l}y = - 6\\x = 8\end{array} \right.\)

TH2: \(\left\{ \begin{array}{l}y + 7 = - 1\\x - 3 = - 5\end{array} \right.\,\,n\^e n\,\,\left\{ \begin{array}{l}y = - 8\\x = - 2\end{array} \right.\)

TH3: \(\left\{ \begin{array}{l}y + 7 = 5\\x - 3 = 1\end{array} \right.\,\,n\^e n\,\,\left\{ \begin{array}{l}y = - 2\\x = 4\end{array} \right.\)

TH4: \(\left\{ \begin{array}{l}y + 7 = - 5\\x - 3 = - 1\end{array} \right.\,\,n\^e n\,\,\left\{ \begin{array}{l}y = - 12\\x = 2\end{array} \right.\)