Question

Tìm số nguyên x, y biết x²y-x+xy=6

Answer 1

\(xy\left(x+1\right)-x-1=5\)\(\Leftrightarrow xy\left(x+1\right)-\left(x+1\right)=5\)

\(\Leftrightarrow\left(x+1\right)\left(xy-1\right)=5=5.1=1.5\)số nguyễn thị thêm (-) nữa

\(\orbr{\begin{cases}x+1=1=>x=0\\xy-1=5=>\left(loai\right)\end{cases}}\)\(\hept{\begin{cases}x+1=5=>x=4\\4y-1=5=>y=\frac{6}{4}\left(loai\right)\end{cases}}\)

\(\hept{\begin{cases}x+1=-1=>x=-2\\-2y-1=-5=>y=2\left(nhan\right)\end{cases}}\)

\(\hept{\begin{cases}x+1=-5=>x=-6\\-6.y-1=-1=>y=0\end{cases}}\)

KL:

x,y=(-2,2)

x,y=(-6,0)