\(A=\left|2018-x\right|+\left|x-2017\right|\ge2018-x+x-2017=1\)
dấu = xãy ra khi \(\left(2018-x\right)\left(x-2017\right)\ge0\Leftrightarrow2017\le x\le2018\)
vậy \(A_{min}=1\) khi \(2017\le x\le2018\)
\(B=\left|x-1\right|+\left|2019-x\right|+\left|x-1999\right|\ge x-1+2019-x+\left|x-1999\right|\)
\(B\ge\left|x-1999\right|+2020\ge2020\)
Dấu = xảy ra khi \(\left\{{}\begin{matrix}x-1\ge0\\2019-x\ge0\\x-1999=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}1\le x\le2019\\x=1999\end{matrix}\right.\Rightarrow x=1999\)
vậy \(B_{min}=2020\) khi x=1999
\(A=\left|2018-x\right|+\left|2017-x\right|\)
\(A=\left|2018-x\right|+\left|x-2017\right|\)
Áp dụng BĐT:
\(\left|A\right|+\left|B\right|\ge\left|A+B\right|\)
\(\Rightarrow A\ge\left|2018-x+x-2017\right|\)
\(\Rightarrow A\ge1\)
Dấu "=" xảy ra khi:
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}2018-x\ge0\Rightarrow x\le2018\\x-2017\ge0\Rightarrow x\ge2017\end{matrix}\right.\\\left\{{}\begin{matrix}2018-x< 0\Rightarrow x< 2018\\x-2017< 0\Rightarrow x< 2017\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow2017\le x\le2018\)
B tương tự
| x | x < 2017 | 2017 | 2017<x<2018 | 2018 | x >2018 |
| \(|2018-x|\) | 2018 - x | 1 | 2018 - x | 0 | -2018+x |
| \(|2017-x|\) | 2017 - x | 0 | -2017 + x | 1 | -2017+x |
| A | -2x +4035 | 1 | 1 | 1 | 2x-4035 |
* Nếu x < 2017 thì 2x < 4034 \(\Rightarrow\) -2x > -4034 \(\Rightarrow\) -2x + 2035 > 1
* Nếu x > 2018 thì 2x > 4035 \(\Rightarrow\) 2x - 4035 >1
Do đó: A\(\ge\) 1
Vậy Min A = 1 ( khi 2017 < x< 2018 )
A=/2018-x/+/2017-x/=2018-x+x-2017=1
vậy biểu thúc A có gtnn là 1
B=/x-1/+/x-1999/+/x-2019/
= x-1+1999-x+2019-x=4017
Vậy biểu thức B có gtnn là 4017
A=|2018−x|+|x−2017|≥2018−x+x−2017=1A=|2018−x|+|x−2017|≥2018−x+x−2017=1
dấu = xãy ra khi (2018−x)(x−2017)≥0⇔2017≤x≤2018(2018−x)(x−2017)≥0⇔2017≤x≤2018
vậy Amin=1Amin=1 khi 2017≤x≤20182017≤x≤2018
B=|x−1|+|2019−x|+|x−1999|≥x−1+2019−x+|x−1999|B=|x−1|+|2019−x|+|x−1999|≥x−1+2019−x+|x−1999|
B≥|x−1999|+2020≥2020B≥|x−1999|+2020≥2020
Dấu = xảy ra khi ⎧⎪⎨⎪⎩x−1≥02019−x≥0x−1999=0⇔{1≤x≤2019x=1999⇒x=1999{x−1≥02019−x≥0x−1999=0⇔{1≤x≤2019x=1999⇒x=1999
vậy Bmin=2020Bmin=2020 khi x=1999
