Question

Tìm GTNN:

Answer 1

`b)sqrt{4x^2-24x+45}`

`=sqrt{(2x)^2-2.2x.6+36+9}`

`=sqrt{(2x-6)^2+9}`

Vì `(2x-6)^2>=0=>(2x-6)^2+9>=9`

`=>sqrt{(2x-6)^2+9}>=sqrt9=3`

Dấu "=" xảy ra khi `2x-6=0<=>2x=6<=>x=3`

Vậy `GTLN{sqrt{4x^2-24x+45}}=3<=>x=3`

Answer 2

\(\sqrt{4x^2-24x+45}=\sqrt{4\left(x-3\right)^2+9}\) 

Vì \(4\left(x-3\right)^2\ge0\Rightarrow4\left(x-3\right)^2+9\ge9\)

\(\Rightarrow\sqrt{4x^2-24x+45}\ge\sqrt{9}=3\)

\(ĐTXR\Leftrightarrow x=3\)