Question

Aflati x si y numere intregi, stiind ca (x-1)(y+1)=17

Va rog, ajutati-ma cu aceasta problema!​

Answer 1

$\it (x-1)(y+1)=17=(-17)\cdot(-1)=(-1)\cdot(-17)=1\cdot17=17\cdot1 \Rightarrow\\ \\ \\ \Rightarrow\begin{cases}\it x-1\in\{-17,-1,\ 1,\ 17\}|_{+1}\Rightarrow x\in\{-16,\ 0,\ \ 2,\ 18\}\ \ \ \ \ (1)\\ \\ \it y+1\in\{-1,-17,\ 17,\ 1\}|_{-1}\Rightarrow x\in\{-2,\ -18,\ 16,\ 0\}\ \ \ \ \ (2)\end{cases}\\ \\ \\ \\ (1),\ (2) \Rightarrow (x,\ y) \in \{(-16,\ -2),\ (0,\ -18),\ (2,\ 16),\ (18,\ 0)\}$