a) Ta có: \(\left(x^2+7\right)\left(x^2-49\right)< 0\)
\(\Rightarrow x^2+7;x^2-49\) khác dấu
*Trường hợp 1:
\(\left\{{}\begin{matrix}x^2+7< 0\\x^2-49>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^2< -7\\x^2>49\end{matrix}\right.\)(loại)
*Trường hợp 2:
\(\left\{{}\begin{matrix}x^2+7>0\\x^2-49< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^2>-7\\x^2< 49\end{matrix}\right.\Leftrightarrow x\in\left\{0;-1;1;2;-2;3;-3;4;-4;5;-5;6;-6\right\}\)
Vậy: \(x\in\left\{0;1;-1;2;-2;3;-3;4;-4;5;-5;6;-6\right\}\)
b) Ta có: (2x-1)(2y+1)=-35
\(\Leftrightarrow\)2x-1; 2y+1\(\in\)Ư(-35)
\(\Leftrightarrow\)2x-1; 2y+1\(\in\){1;-1;5;-5;7;-7;35;-35}
*Trường hợp 1:
\(\left\{{}\begin{matrix}2x-1=1\\2y+1=-35\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=2\\2y=-36\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-18\end{matrix}\right.\)(thỏa mãn)
*Trường hợp 2:
\(\left\{{}\begin{matrix}2x-1=-35\\2y+1=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-34\\2y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-17\\y=0\end{matrix}\right.\)(thỏa mãn)
*Trường hợp 3:
\(\left\{{}\begin{matrix}2x-1=-1\\2y+1=35\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=0\\2y=34\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=17\end{matrix}\right.\)(thỏa mãn)
*Trường hợp 4:
\(\left\{{}\begin{matrix}2x-1=35\\2y+1=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=36\\2y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=18\\y=-1\end{matrix}\right.\)(thỏa mãn)
*Trường hợp 5:
\(\left\{{}\begin{matrix}2x-1=5\\2y+1=-7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=6\\2y=-8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-4\end{matrix}\right.\)(thỏa mãn)
*Trường hợp 6:
\(\left\{{}\begin{matrix}2x-1=-7\\2y+1=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-6\\2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=2\end{matrix}\right.\)(thỏa mãn)
*Trường hợp 7:
\(\left\{{}\begin{matrix}2x-1=-5\\2y+1=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-4\\2y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=3\end{matrix}\right.\)(thỏa mãn)
*Trường hợp 8:
\(\left\{{}\begin{matrix}2x-1=7\\2y+1=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=8\\2y=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=-3\end{matrix}\right.\)
Vậy: x∈{1;-17;0;18;3;-3;-2;4} và y∈{-18;0;17;-1;-4;2;3;-3}
