Question

Tìm các cặp số x,y nguyên thoả mản:x+2y=3xy+3

Answer 1

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

\(\Leftrightarrow3xy-x-2y+3=0\)

\(\Leftrightarrow9xy-3x-6y+9=0\)

\(\Leftrightarrow3x\left(3y-1\right)-2\left(3y-1\right)+7=0\)

\(\Leftrightarrow\left(3x-2\right)\left(3y-1\right)=-7\)

3x-2	-7	-1	1	7
3y-1	1	7	-7	-1
x	-5/3(ktm)	1/3(ktm)	1	3
y	2/3(ktm)	8/3(ktm)	-2	0

Vậy \(\left(x;y\right)=\left(1;-2\right);\left(3;0\right)\)