A=\(\dfrac{5}{4-|x-1|}\)
Vì \(|x-1|\ge0\Leftrightarrow-|x-1|\le0\Leftrightarrow4-|x-1|\le4\)
\(\Rightarrow\dfrac{1}{4-|x-1|}\ge\dfrac{1}{4}\)\(\Leftrightarrow\dfrac{5}{4-|x-1|}\ge\dfrac{5}{4}\)
Vậy GTLN của A là \(\dfrac{5}{4}\)\(\Leftrightarrow|x-1|=0\Leftrightarrow x-1=0\Leftrightarrow x=1\)
B=\(\dfrac{10}{2-\left(x-2\right)^2}\)
Vì \(\left(x-2\right)^2\ge0\Leftrightarrow-\left(x-2\right)\le0\Leftrightarrow2-\left(x-2\right)\le2\)
\(\Rightarrow\dfrac{1}{2-\left(x-2\right)^2}\ge\dfrac{1}{2}\Leftrightarrow\dfrac{10}{2-\left(x-2\right)^2}\ge\dfrac{10}{2}\Leftrightarrow\dfrac{10}{2-\left(x-2\right)^2}\ge5\)Vậy GTLN của B là 5\(\Leftrightarrow\left(x-2\right)^2=0\Leftrightarrow x-2=0\Leftrightarrow x=2\)
