Question

Tìm x, y thuộc Z để cho : x - y + 2xy = 3

Answer 1

\(x-y+2xy=3\)

\(\Leftrightarrow x+2xy-y=3\)

\(\Leftrightarrow x\left(1+2y\right)-\frac{1}{2}\left(1+2y\right)+\frac{1}{2}=3\)

\(\Leftrightarrow\left(1+2y\right)\left(x-\frac{1}{2}\right)=3-\frac{1}{2}\)

\(\Leftrightarrow\left(1+2y\right)\left(x-\frac{1}{2}\right)=\frac{5}{2}\)

\(\Leftrightarrow2.\left(1+2y\right)\left(x-\frac{1}{2}\right)=\frac{5}{2}.2\) (Nhân mỗi vế với 2)

\(\Rightarrow\left(1+2y\right)\left(2x-1\right)=5\)

\(\Rightarrow1+2y\)và \(2x-1\)\(\inƯ\left(5\right)=\left\{1;5;-1;-5\right\}\)

Ta có bảng giá trị sau:

\(1+2y\)	\(1\)	\(5\)	\(-1\)	\(-5\)
\(y\)	\(0\)	\(2\)	\(-1\)	\(-3\)
\(2x-1\)	\(5\)	\(1\)	\(-5\)	\(-1\)
\(x\)	\(3\)	\(1\)	\(-2\)	\(0\)

Vậy \(\left(x;y\right)\in\left\{\left(3;0\right);\left(1;2\right);\left(-2;-1\right);\left(0;-3\right)\right\}\)