Question

[TRịnh Kim Ngân]

 

Answer 1

[HT.Phong (9A5)]

\(\left\{{}\begin{matrix}2x+y=-1\\3y-x=7m-10\end{matrix}\right. \Leftrightarrow\left\{{}\begin{matrix}6x+3y=-3\\-x+3y=7m-10\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}2x+y=-1\\7x=7-7m\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2\left(1-m\right)+y=-1\\x=1-m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-1-2\left(1-m\right)=2m-3\\x=1-m\end{matrix}\right.\)

 \(x^2-2y=\left(1-m\right)^2-\left(2m-3\right)\)

\(=1-2m+m^2-2m+3=m^2-4m+4\\ =\left(m-2\right)^2\)

Ta có: \(\left(m-2\right)^2\ge0\forall m=>x^2-2y\ge0\forall m\)

Dấu "=" xảy ra: \(m-2=0< =>m=2\)

Vậy: \(Min_{x^2-2y}=0< =>m=2\)