a: \(\left|4x-3\right|>=0\forall x\)
\(\left|2y+5\right|>=0\forall y\)
Do đó: \(\left|4x-3\right|+\left|2y+5\right|>=0\forall x,y\)
=>\(A=\left|4x-3\right|+\left|2y+5\right|+1>=1\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}4x-3=0\\2y+5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{4}\\y=-\dfrac{5}{2}\end{matrix}\right.\)
b: \(B=\left|2x-1\right|+\left|2x-9\right|=\left|2x-1\right|+\left|9-2x\right|>=\left|2x-1+9-2x\right|=8\)
Dấu '=' xảy ra khi (2x-1)(2x-9)<=0
=>\(\dfrac{1}{2}< =x< =\dfrac{9}{2}\)
c: \(C=\left|3x-1\right|+3x-10\)
TH1: \(x>=\dfrac{1}{3}\)
=>\(C=3x-1+3x-10=6x-11\)
=>C không có giá trị nhỏ nhất
TH2: \(x< \dfrac{1}{3}\)
=>\(C=1-3x+3x-10=-9\)
=>\(C_{min}=-9\) khi \(x< \dfrac{1}{3}\)
