\(\left|2x-5\right|+\left|xy-3y+2\right|=0\)
Do \(\left|2x-5\right|,\left|xy-3y+2\right|\ge0\)
\(\Rightarrow\left\{{}\begin{matrix}\left|2x-5\right|=0\\\left|xy-3y+2\right|=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-5=0\\xy-3y+2=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=4\end{matrix}\right.\)
Ta có: \(\left|2x-5\right|\ge0\forall x\)
\(\left|xy-3y+2\right|\ge0\forall x,y\)
Do đó: \(\left|2x-5\right|+\left|xy-3y+2\right|\ge0\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x=\dfrac{5}{2}\\\dfrac{5}{2}y-3y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=4\end{matrix}\right.\)
