Đáp án:
Giải thích các bước giải:
$ PT ⇔ 4x² + 4x + 52 = 4y²$
$ ⇔ (2x + 1)² - 4y² = - 51$
$ ⇔ (2x - 2y + 1)(2x + 2y + 1) = - 51$
TH1$: \left[ \begin{array}{l}2x - 2y + 1= - 1\\2x + 2y + 1= 51\end{array} \right. ⇔ \left[ \begin{array}{l}x = 12\\y = 13\end{array} \right.$
TH2$: \left[ \begin{array}{l}2x - 2y + 1 = 1\\2x + 2y + 1= - 51\end{array} \right. ⇔ \left[ \begin{array}{l}x = - 13\\y = - 13\end{array} \right.$
TH3$: \left[ \begin{array}{l}2x - 2y + 1= - 51\\2x + 2y + 1= 1\end{array} \right. ⇔ \left[ \begin{array}{l}x = - 13\\y = 13\end{array} \right.$
TH4$: \left[ \begin{array}{l}2x - 2y + 1= 51\\2x + 2y + 1= - 1\end{array} \right. ⇔ \left[ \begin{array}{l}x = 12\\y = - 13\end{array} \right.$
TH5$: \left[ \begin{array}{l}2x - 2y + 1= - 3\\2x + 2y + 1= 17\end{array} \right. ⇔ \left[ \begin{array}{l}x = 3\\y = 5\end{array} \right.$
TH6$: \left[ \begin{array}{l}2x - 2y + 1= 3\\2x + 2y + 1= - 17\end{array} \right. ⇔ \left[ \begin{array}{l}x = - 4\\y = - 5\end{array} \right.$
TH7$: \left[ \begin{array}{l}2x - 2y + 1= - 17\\2x + 2y + 1= 3\end{array} \right. ⇔ \left[ \begin{array}{l}x = - 4\\y = 5\end{array} \right.$
TH8$: \left[ \begin{array}{l}2x - 2y + 1= 17\\2x + 2y + 1= - 3\end{array} \right. ⇔ \left[ \begin{array}{l}x = 3\\y = - 5\end{array} \right.$
