Question

tìm tất cả các cặp (x,y) thoả mãn 2013x^2+2014y^2-4026x+4028y+4027=0

Answer 1

\(\Leftrightarrow2013\left(x^2-2x+1\right)+2014\left(y^2+2y+1\right)=0\)

\(\Leftrightarrow2013\left(x-1\right)^2+2014\left(y+1\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\y+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)