|
|
b)
$\left\{ \begin{array}{l} x + y +x^{2} + y^{2}= 8\\ xy( x+ 1)(y + 1) = 12\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} x(x+1)+y(y+1)=8\\ x(x+1)y(y+1)=12 \end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} x(x+1)=2\\ y(y+1)=6 \end{array} \right.\\ \left\{ \begin{array}{l} x(x+1)=6\\ y(y+1)=2 \end{array} \right. \end{array} \right.$
Từ đó suy ra nghiệm:
$(x;y)\in\{(1;2),(1;-3),(-2;2),(-2;-3),(2;1),(-3;1),(2;-2),(-3;-2)\}$
|