Question

1.Tìm x,y thuộc Z biết:

a)\(XY+5X+Y=8\)

b)\(\left(2X-6\right).\left(4Y+8\right)=32\)

Đoàn Đức Hiếu

Answer 1

\(xy+5x+y=8\)

\(\Rightarrow xy+5x+y+5=13\)

\(\Rightarrow x\left(y+5\right)+1\left(y+5\right)=13\)

\(\Rightarrow\left(x+1\right)\left(y+5\right)=13\)

\(\Rightarrow x+1;y+5\inƯ\left(13\right)\)

\(Ư\left(13\right)=\left\{\pm1;\pm13\right\}\)

\(\Rightarrow\left\{{}\begin{matrix}x+1=1\Rightarrow x=0\\y+5=13\Rightarrow y=8\\x+1=-1\Rightarrow x=-2\\y+5=-13\Rightarrow y=-18\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x+1=13\Rightarrow x=12\\y+5=1\Rightarrow y=-4\\x+1=-13\Rightarrow x=-14\\y+5=-1\Rightarrow y=6\end{matrix}\right.\)