tìm x,y ∈ Z bt: c) x(y+1)+y=18 d) x ²+xy+xy=9 17/11/2021 Bởi Madelyn tìm x,y ∈ Z bt: c) x(y+1)+y=18 d) x ²+xy+xy=9
Đáp án: `c)` ` x(y+1) + y = 18` ` x(y+1) + (y+1) = 19` ` (x+1)(y+1) = 19` ` => x +1 ; y +1` thuộc `Ư(19)` Ta có bảng sau \begin{array}{|c|c|c|}\hline x+1&1&19&-1&-19\\\hline y+1&19&1&-19&-1\\\hline x&0&18&-2&-20\\\hline y&18&0&-20&-2 \\\hline\end{array} Vậy ` (x;y) ∈ {(0;18); (18;0); (-2;-20); (-20;-2)}` `d)` ` x^2+ xy +xy= 9` ` => x^2+ 2xy = 9` ` => x(x+2y) = 9` ` => x ; x +2y ∈ Ư(9)` Ta có bảng sau \begin{array}{|c|c|c|}\hline x&1&9&-1&-9\\\hline x+2y&9&1&-9&-1\\\hline y&4&-4&-4&4 \\\hline\end{array} Vậy ` (x;y) ∈ {(1;4); (9;-4); (-1;-4); (-9;4)}` Bình luận
Đáp án:
`c)`
` x(y+1) + y = 18`
` x(y+1) + (y+1) = 19`
` (x+1)(y+1) = 19`
` => x +1 ; y +1` thuộc `Ư(19)`
Ta có bảng sau
\begin{array}{|c|c|c|}\hline x+1&1&19&-1&-19\\\hline y+1&19&1&-19&-1\\\hline x&0&18&-2&-20\\\hline y&18&0&-20&-2 \\\hline\end{array}
Vậy ` (x;y) ∈ {(0;18); (18;0); (-2;-20); (-20;-2)}`
`d)`
` x^2+ xy +xy= 9`
` => x^2+ 2xy = 9`
` => x(x+2y) = 9`
` => x ; x +2y ∈ Ư(9)`
Ta có bảng sau
\begin{array}{|c|c|c|}\hline x&1&9&-1&-9\\\hline x+2y&9&1&-9&-1\\\hline y&4&-4&-4&4 \\\hline\end{array}
Vậy ` (x;y) ∈ {(1;4); (9;-4); (-1;-4); (-9;4)}`