Question

tìm x, y thoả mãn điều kiện: 2x² + y² = 4x -2xy - 4

Answer 1

\(\Leftrightarrow\left(x^2+2xy+y^2\right)+\left(x^2-4x+4\right)=0\)

\(\Leftrightarrow\left(x+y\right)^2+\left(x-2\right)^2=0\)

Do \(\left\{{}\begin{matrix}\left(x+y\right)^2\ge0\\\left(x-2\right)^2\ge0\end{matrix}\right.\) ;\(\forall x;y\)

\(\Rightarrow\left(x+y\right)^2+\left(x-2\right)^2\ge0;\forall x;y\)

Dấu "=" xảy ra khi và chỉ khi:

\(\left\{{}\begin{matrix}x+y=0\\x-2=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=2\\y=-2\end{matrix}\right.\)