Đáp án: a ) xy ∈ [ (4,12);(10,6);(2,-2);(-4,4) ]
b ) xy ∈ [ (2,5);(6,1);(0,Z);(-4,-1) ]
Giải thích các bước giải:
a ) ( x - 3 )( y - 5 ) = 7
Ta thấy : 7 = 7 . 1 = ( -7 )( -1 )
TH 1 : \(\left[ \begin{array}{l}x-3=1\\y-5=7\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=4\\y=12\end{array} \right.\)
TH 2 : \(\left[ \begin{array}{l}x-3=7\\y-5=1\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=10\\y=6\end{array} \right.\)
TH 3 : \(\left[ \begin{array}{l}x-3=-1\\y-5=-7\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=2\\y=-2\end{array} \right.\)
TH 4 : \(\left[ \begin{array}{l}x-3=-7\\y-5=-1\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=-4\\y=4\end{array} \right.\)
b ) ( x - 1 )( xy - 5 ) = 5
Ta thấy : 5 = 5 . 1 = ( -5 )(-1)
TH 1 : \(\left[ \begin{array}{l}x-1=1\\xy-5=5\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=2\\xy=10\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=2\\2y=10\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=2\\y=5\end{array} \right.\)
TH 2 : \(\left[ \begin{array}{l}x-1=5\\xy-5=1\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=6\\xy=6\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=6\\6y=6\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=6\\y=1\end{array} \right.\)
TH 3 : \(\left[ \begin{array}{l}x-1=-1\\xy-5=-5\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=0\\xy=0\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=0\\0y=0\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=0\\y=Z\end{array} \right.\)
TH 4 : \(\left[ \begin{array}{l}x-1=-5\\xy-5=-1\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=-4\\xy=4\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=-4\\-4y=4\end{array} \right.\)
→ \(\left[ \begin{array}{l}x=-4\\y=-1\end{array} \right.\)
