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![](https://rs.olm.vn/images/avt/0.png?1311)
các bạn giúp mik với. Đề trên kia là \(\sqrt{x}+2021\) nhé! Mik đánh sai
![](https://rs.olm.vn/images/avt/0.png?1311)
Với x ≥ 0 thì \(\sqrt{x}\ge0\) nên \(\sqrt{x}+1\ge1\)
Khi đó \(B=\left(\sqrt{x}+1\right)^{99}+2022\ge1^{99}+2022\)
Hay \(B=\left(\sqrt{x}+1\right)^{99}+2022\ge2023\)
Dấu "=" xảy ra khi \(\sqrt{x}=0\) hay x = 0
Vậy GTNN của \(B=\left(\sqrt{x}+1\right)^{99}+2022\) là 2023 khi x = 0
\(B=\left(\sqrt{x}+1\right)^{99}+2022\left(x\ge0\right)\)
Vì: \(x\ge0\)
Nên => \(\left(\sqrt{x}+1\right)^{99}\ge0\)
=> \(\left(\sqrt{x}+1\right)^{99}+2022\ge2022\)
=> \(B\ge2022\)
Dấu " = " xảy ra khi: \(\Leftrightarrow\sqrt{x}+1=0\Leftrightarrow\sqrt{x}=-1\left(voli\right)\)
Vậy: B không có giá trị nhỏ nhất
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{\sqrt{x+2021}}{\sqrt{x+2022}}\)
= \(\sqrt{x^1+}2021^1\)
= \(\sqrt{x^1+2022^1}\)
= \(2022^3\)- \(2021^3\)
= \(1^3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left|2021-x\right|+\dfrac{1}{2}\left|4040-2x\right|\)
\(A=\left|2021-x\right|+\left|2020-x\right|\)
\(A=\left|2021-x\right|+\left|x-2020\right|\ge\left|2021-x+x-2020\right|=1\)
\(A_{min}=1\) khi \(2020\le x\le2021\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{3\left(\sqrt{x}+1\right)-2}{2\left(\sqrt{x}+1\right)}=\dfrac{3}{2}-\dfrac{1}{\sqrt{x}+1}\)
Ta có \(\sqrt{x}+1\ge1\Leftrightarrow-\dfrac{1}{\sqrt{x}+1}\ge-1\)
\(\Leftrightarrow A\ge\dfrac{3}{2}-1=\dfrac{1}{2}\)
Dấu \("="\Leftrightarrow x=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{2}{3}-\left|\dfrac{3}{4}\right|+\sqrt{\dfrac{25}{9}}-\left(\dfrac{2021}{2022}\right)^0=\dfrac{2}{3}-\dfrac{3}{4}+\dfrac{5}{3}-1=\dfrac{7}{12}\)
\(=\dfrac{2}{3}-\dfrac{3}{4}+\dfrac{5}{3}-1=\dfrac{7}{12}\)
Sửa: \(Đk:x\ge0\)
\(C=1-\dfrac{1}{\sqrt{x}+2022}\ge1-\dfrac{1}{0+2022}=\dfrac{2021}{2022}\\ C_{min}=\dfrac{2021}{2022}\Leftrightarrow x=0\)
\(C=\dfrac{\sqrt{x}+2022}{\sqrt{x}+2022}-\dfrac{1}{\sqrt{x}+2022}=1-\dfrac{1}{\sqrt{x}+2022}\)
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 \(\Leftrightarrow x=0\)