Question

Tìm số nguyên x,y sao cho x-2xy+y=0

Answer 1

\(x-2xy+y=0\)

\(\Leftrightarrow2x-4xy+2y=0\)

\(\Leftrightarrow2x-2y\left(2x-1\right)=0\)

\(\Leftrightarrow2x-1-2y\left(2x-1\right)=-1\)

\(\Leftrightarrow\left(2x-1\right)\left(1-2y\right)=-1\)

Nếu \(2x-1=1\) thì \(1-2y=-1\) \(\Rightarrow x=1\) thì \(y=1\)

Nếu \(2x-1=-1\) thì \(1-2y=1\) \(\Rightarrow x=0\) thì \(y=0\)

Vậy \(\left(x;y\right)=\left(0;0\right);\left(1;1\right)\)