a: \(\left|x-y-2\right|>=0\forall x,y\)
\(\left|y+3\right|>=0\forall y\)
Do đó: \(\left|x-y-2\right|+\left|y+3\right|>=0\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}y+3=0\\x-y-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-3\\x=y+2=-3+2=-1\end{matrix}\right.\)
b: \(\left|x-2y\right|>=0\forall x,y\)
\(\left(y+4\right)^2>=0\forall y\)
Do đó: \(\left|x-2y\right|+\left(y+4\right)^2>=0\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-2y=0\\y+4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-4\\x=2y=2\cdot\left(-4\right)=-8\end{matrix}\right.\)
c: \(\left|x-y-4\right|>=0\forall x,y\)
\(\left|y-1\right|>=0\forall y\)
Do đó: \(\left|x-y-4\right|+\left|y-1\right|>=0\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}y-1=0\\x-y-4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=y+4=1+4=5\end{matrix}\right.\)
d: \(\left|2x-y-1\right|>=0\forall x,y\)
\(\left|x-1\right|>=0\forall x\)
Do đó: \(\left|2x-y-1\right|+\left|x-1\right|>=0\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}2x-y-1=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2x-1=2\cdot1-1=1\end{matrix}\right.\)
