Question

[Nguyễn Tuyết Minh]

Tìm GTNN của : C = \(\dfrac{\sqrt{x}+2021}{\sqrt{x}+2022}\)( với x khác 0)

Answer 1

[Nguyễn Hoàng Minh]

Sửa: \(Đk:x\ge0\)

\(C=1-\dfrac{1}{\sqrt{x}+2022}\ge1-\dfrac{1}{0+2022}=\dfrac{2021}{2022}\\ C_{min}=\dfrac{2021}{2022}\Leftrightarrow x=0\)

Answer 2

[Lấp La Lấp Lánh]

\(C=\dfrac{\sqrt{x}+2022}{\sqrt{x}+2022}-\dfrac{1}{\sqrt{x}+2022}=1-\dfrac{1}{\sqrt{x}+2022}\)

Do \(\sqrt{x}+2022\ge2022\Leftrightarrow\dfrac{1}{\sqrt{x}+2022}\le\dfrac{1}{2022}\Leftrightarrow-\dfrac{1}{\sqrt{x}+2022}\ge-\dfrac{1}{2022}\)

\(\Leftrightarrow C=1-\dfrac{1}{\sqrt{x}+2022}\ge1-\dfrac{1}{2022}=\dfrac{2011}{2022}\)

Dấu"=" xảy ra \(\Leftrightarrow x=0\)