\(x^2-4xy+5y^2+6x-10y+10=0\)
\(x^2-2x\left(2y-3\right)+5y^2-10y+10=0\)
\(x^2-2x\left(2y-3\right)+\left(4y^2-12x+9\right)+\left(y^2+2x+1\right)=0\)
\(x^2-2x\left(2y-3\right)+\left(2y-3\right)^2+\left(y+1\right)^2=0\)
\(\left(x-2y+3\right)^2+\left(y+1\right)^2=0\)
Ta có: \(\hept{\begin{cases}\left(x-2y+3\right)^2\ge0\forall x;y\\\left(y+1\right)^2\ge0\forall y\end{cases}}\)\(\Rightarrow\left(x-2y+3\right)^2+\left(y+1\right)^2\ge0\forall x;y\)
Mà \(\left(x-2y+3\right)^2+\left(y+1\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(x-2y+3\right)^2=0\\\left(y+1\right)^2=0\end{cases}\Leftrightarrow\hept{\begin{cases}x-2y+3=0\\y+1=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x-2y+3=0\\y=-1\end{cases}\Leftrightarrow}\hept{\begin{cases}x+2+3=0\\y=-1\end{cases}\Leftrightarrow}\hept{\begin{cases}x=-5\\y=-1\end{cases}}}\)Vậy \(\hept{\begin{cases}x=-5\\y=-1\end{cases}}\)
Tham khảo nhé~
Sao anh kudo không tách thẳng như vầy luôn cho nhanh?(nhanh hơn đúng 1 dòng ở phần phân tích thôi:v)
\(A=x^2-4xy+5y^2+6x-10y+10=0\)
\(\Leftrightarrow\left(x^2-2.x.2y+4y^2\right)+\left(6x-12y\right)+9+\left(y^2+2y+1\right)=0\)
\(\Leftrightarrow\left[\left(x-2y\right)^2+2.\left(x-2y\right).3+3^2\right]+\left(y+1\right)^2=0\)
\(\Leftrightarrow\left(x-2y+3\right)^2+\left(y+1\right)^2=0\)
Đến đây ez rồi!
