$c$) $x(y+1)+y=18$
$⇔ x(y+1) + (y+1) = 19$
$⇔ (x+1)(y+1)=19$
$⇒ x+1;y+1$ $∈$ `Ư(19)={±1;±19}` vì $x;y ∈ Z$
Ta có bảng:
$\left[\begin{array}{ccc}x+1&-19&-1&1&19\\y+1&-1&-19&19&1\\x&-20&-2&0&18\\y&-2&-20&18&0\end{array}\right]$
Vậy `(x;y)=(-20;-2);(-2;-20);(0;18);(18;0)`.
$d$) $x^2 + xy + xy = 9$
$⇔ x^2 + 2xy = 9$
$⇔ x(x+2y) = 9$
$⇒$ $x;x+2y$ $∈$ `Ư(9)={±1;±3;±9}` vì $x;y ∈ Z$
Ta có bảng:
$\left[\begin{array}{ccc}x&-9&-3&-1&1&3&9\\x+2y&-1&-3&-9&9&3&1\\y&4&0&-4&4&0&-4\end{array}\right]$
Vậy `(x;y)=(-9;4);(-3;0);(-1;-4);(1;4);(3;0);(9;-4)`.
