a)\(5x^2+13y^2+6xy=12x-4y\)
\(\Leftrightarrow5x^2+6x\left(y-2\right)+13y^2+4y=0\)
pt có nghiệm:\(\Delta'=9\left(y-2\right)^2-65y^2-20y\ge0\)
\(\Leftrightarrow9y^2-36y+36-65y^2-20y\ge0\)
\(\Leftrightarrow-56y^2-56y+36\ge0\)
Mà \(y\in Z\)\(\Rightarrow-1\le y\le0\)
\(\Rightarrow y=0;1\)
Thay vào tìm x
Nốt câu b:
\(x^3+y^3+3xy\left(x+y\right)-3xy\left(x+y\right)-6xy-1=0\)
\(\Leftrightarrow\left(x+y\right)^3-3xy\left(x+y+2\right)+1=0\)
\(\Leftrightarrow\left(x+y\right)^3+8-3xy\left(x+y+2\right)-7=0\)
\(\Leftrightarrow\left(x+y+2\right)\left(x^2+y^2+2xy-2x-2y+4\right)-3xy\left(x+y+2\right)=7\)
\(\Leftrightarrow\left(x+y+2\right)\left(x^2+y^2-xy-2x-2y+4\right)=7\)
\(\Leftrightarrow...\)
