2x\(^2\)+y\(^2\)+3xy+3x+2y+2=0
\(\Leftrightarrow\)16x\(^2\)+8y\(^2\)+24xy+24x+16y+16=0
\(\Leftrightarrow\)(4x)\(^2\)+24x(y+1)+8y\(^2\)+16y+16=0
\(\Leftrightarrow\)(4x)\(^2\)+24x(y+1)+[3(y+1)]\(^2\)-[3(y+1)]\(^2\)+8y\(^2\)+16y+16=0
\(\Leftrightarrow\)(4x+3y+3)\(^2\)-9y\(^2\)-18y-9+8y\(^2\)16y+16=0
\(\Leftrightarrow\)(4x+3y+3)\(^2\)-y\(^2\)-2y-1+8=0
\(\Leftrightarrow\)(4x+3y+3)\(^2\)- (y+1)\(^2\)= -8
\(\Leftrightarrow\)(y+1+4x+3y+3) (y+1-4x-3y-3)=8
\(\Leftrightarrow\)4(x+y+4) (-4-2y-2)=8
\(\Leftrightarrow\)(x+y+4) (2x+y+11)= -1
\(\Leftrightarrow\){x+y+4= -1
{2x+y+1=1
\(\Rightarrow\)x=2 và y= -4
{x+y+4= 1
{2x+y+1= -1
\(\Rightarrow\)x=-2 và y=2
vậy nghiệm (x,y)=(-2;4) (-2;2)
