`B=x-2\sqrt{x-2}+2022`
`B=(\sqrt{x-2})^2-2\sqrt{x-2}+1+2023`
`B=(\sqrt{x-2}-1)^2+2023`
Vì `x >= 2<=>(\sqrt{x-2}-1)^2 >= 0 AA x`
`<=>(\sqrt{x-2}-1)^2+2023 >= 2023 AA x`
Hay `B >= 2023 AA x`
Dấu "`=`" xảy ra `<=>(\sqrt{x-2}-1)^2=0`
`<=>\sqrt{x-2}=1`
`<=>x-2=1<=>x=3` (t/m)
Vậy với `x=3` thì `B` đạt GTNN là `2023`
\(B=x-2\sqrt{x-2}+2022\)
\(=\left(x-2\right)-2\sqrt{x-2}+1+2023\)
\(=\left(\sqrt{x-2}-1\right)^2+2023\)
Vì \(\left(\sqrt{x-2}-1\right)^2\ge0\forall x\)
\(MinB=2023\Leftrightarrow\sqrt{x-2}=1\Rightarrow x=3\)