Question

Tìm x,y thoả mãn x²+2y²+2xy-14y+49=0

Answer 1

\(\Leftrightarrow\left(x^2+2xy+y^2\right)+\left(y^2-14y+49\right)=0\\ \Leftrightarrow\left(x+y\right)^2+\left(y-7\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x=-y\\y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-7\\y=7\end{matrix}\right.\)

Answer 2

Ta có: x²+2y²+2xy-14y+49=0

      ⇔ (x²+2xy+y²)+(y²-14y+49)=0

      ⇔ (x+y)²+(y-7)²=0

      \(\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\y-7=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-7\\y=7\end{matrix}\right.\)