a) \(A=\sqrt{\left(1+x^2\right)\left(1+y^2\right)+4xy+2\left(x+y\right)\left(1+xy\right)}\)
\(A=\sqrt{1+x^2+y^2+\left(xy\right)^2+4xy+2\left(x+y+x^2y+xy^2\right)}\)
\(A=\sqrt{1+x^2+y^2+\left(xy\right)^2+4xy+2x+2y+2x^2y+2xy^2}\)
\(A=\sqrt{1^2+x^2+y^2+\left(xy\right)^2+2.x.1+2.y.1+2xy+2.xy+2x.xy+2y.xy}\)
\(A=\sqrt{\left(1+x+y+xy\right)^2}\)
\(A=\left|1+x+y+xy\right|=1+x+y+xy\)(vì x,y nguyên dương)
b)A=1+x+y+xy=6
(x+1)+y(x+1)=6
<=> (x+1)(y+1)=6=1.6=2.3=3.2=6.1
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1=1\\y+1=6\end{matrix}\right.\\\left\{{}\begin{matrix}x+1=2\\y+1=3\end{matrix}\right.\\\left\{{}\begin{matrix}x+1=3\\y+1=2\end{matrix}\right.\\\left\{{}\begin{matrix}x+1=6\\y+1=1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=0\\y=5\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\\\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\\\left\{{}\begin{matrix}x=5\\y=0\end{matrix}\right.\end{matrix}\right.\)
vạy (x;y)=(0;5);(1;2);(2;1);(5;0)
