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)}`