Question

l2x-5l + lxy-3y+2l = 0

Answer 1

\(\left|2x-5\right|+\left|xy-3y+2\right|=0\)

Do \(\left|2x-5\right|,\left|xy-3y+2\right|\ge0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|2x-5\right|=0\\\left|xy-3y+2\right|=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-5=0\\xy-3y+2=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=4\end{matrix}\right.\)

Answer 2

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 \(\left\{{}\begin{matrix}x=\dfrac{5}{2}\\\dfrac{5}{2}y-3y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=4\end{matrix}\right.\)