S=|x+y|+2.|y-2|+1998
Ta có\(\left\{{}\begin{matrix}\left|x+y\right|\ge0\\\left|y-2\right|\ge0\end{matrix}\right.\forall xy\)
⇔ \(\left\{{}\begin{matrix}\left|x+y\right|\ge0\\2.\left|y-2\right|\ge0\end{matrix}\right.\forall xy\)
\(\Leftrightarrow\left|x+y\right|+2.\left|y-2\right|\ge0\forall xy\)
\(\Leftrightarrow\left|x+y\right|+2.\left|y-2\right|+1998\ge1998\forall xy\)
\(\Leftrightarrow S\ge1998\forall xy\)
Dấu "=" xảy ra ⇔ \(\left\{{}\begin{matrix}\left|x+y\right|=0\\\left|y-2\right|=0\end{matrix}\right.\)
⇔ \(\left\{{}\begin{matrix}x+y=0\\y+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\y=-2\end{matrix}\right.\)
⇔ \(\left\{{}\begin{matrix}x-2=0\\y=-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-2\end{matrix}\right.\)
Vậy Min A = 1998 \(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-2\end{matrix}\right.\)
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#Chiyuki Fujito
