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\(\frac{x+1}{2019}+\frac{x+2}{2018}+\frac{x+3}{2017}=\frac{x-1}{2021}+\frac{x-2}{2022}+\frac{x-3}{2023}\)
\(\Leftrightarrow\left(\frac{x+1}{2019}+1\right)+\left(\frac{x+2}{2018}+1\right)+\left(\frac{x+3}{2017}+1\right)=\left(\frac{x-1}{2021}+1\right)+\left(\frac{x-2}{2022}+1\right)+\left(\frac{x-3}{2023}+1\right)\)
\(\Leftrightarrow\left(\frac{x+1+2019}{2019}\right)+\left(\frac{x+2+2018}{2018}\right)+\left(\frac{x+3+2017}{2017}\right)=\left(\frac{x-1+2021}{2021}\right)+\left(\frac{x-2+2022}{2022}\right)+\left(\frac{x-3+2023}{2023}\right)\)
\(\Leftrightarrow\frac{x+2020}{2019}+\frac{x+2020}{2018}+\frac{x+2020}{2017}=\frac{x+2020}{2021}+\frac{x+2020}{2022}+\frac{x+2020}{2023}\)
\(\Leftrightarrow\frac{x+2020}{2019}+\frac{x+2020}{2018}+\frac{x+2020}{2017}-\frac{x+2020}{2021}-\frac{x+2020}{2022}-\frac{x+2020}{2023}=0\)
\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2021}-\frac{1}{2022}-\frac{1}{2023}\right)=0\)
Vì \(\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2021}-\frac{1}{2022}-\frac{1}{2023}\ne0\)
=> x + 2020 = 0
=> x = -2020
Bài làm :
Ta có :
\(\frac{x+1}{2019}+\frac{x+2}{2018}+\frac{x+3}{2017}=\frac{x-1}{2021}+\frac{x-2}{2022}+\frac{x-3}{2023}\)
\(\Leftrightarrow\left(\frac{x+1}{2019}+1\right)+\left(\frac{x+2}{2018}+1\right)+\left(\frac{x+3}{2017}+1\right)=\left(\frac{x-1}{2021}+1\right)+\left(\frac{x-2}{2022}+1\right)+\left(\frac{x-3}{2023}+1\right)\)
\(\Leftrightarrow\left(\frac{x+1+2019}{2019}\right)+\left(\frac{x+2+2018}{2018}\right)+\left(\frac{x+3+2017}{2017}\right)=\left(\frac{x-1+2021}{2021}\right)+\left(\frac{x-2+2022}{2022}\right)+\left(\frac{x-3+2023}{2023}\right)\)
\(\Leftrightarrow\frac{x+2020}{2019}+\frac{x+2020}{2018}+\frac{x+2020}{2017}=\frac{x+2020}{2021}+\frac{x+2020}{2022}+\frac{x+2020}{2023}\)
\(\Leftrightarrow\frac{x+2020}{2019}+\frac{x+2020}{2018}+\frac{x+2020}{2017}-\frac{x+2020}{2021}-\frac{x+2020}{2022}-\frac{x+2020}{2023}=0\)
\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2021}-\frac{1}{2022}-\frac{1}{2023}\right)=0\)
\(\text{Vì : }\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2021}-\frac{1}{2022}-\frac{1}{2023}\ne0\)
\(\Rightarrow x+2020=0\Leftrightarrow x=-2020\)
Vậy x=-2020
Tìm giá trị nhỏ nhất
A=|x-2019|+|x-1|
B=|1+ x2|+2019
HELP ME!!!!!!LÀM ĐÚNG MK CHO 5 K, MAI NỘP RỒI T-T
a) Ta có:A=|x-2019| +|x-1|
=|2019-x| +|x-1|
≥|2019-x+x-1|=|2018|=2018
Dấu "=" xảy ra <=> (2019-x)(x-1) ≥0 <=> 1≤x≤2019
b)Ta có:1+x2 ≥0 với mọi x
=> |1+x2| = 1+x2
Do đó: B=|1+x2|+2019 =x2+2020 ≥2020
Dấu "=" xảy ra <=> x=0
Nhớ k mik nha :))))
Mình làm câu a, b gộp lại 1 chỗ luôn nha cậu:vvvv (tại nó thực hiện dc cùng lúc, mà nếu k mk tách ở phần dưới nha)
P(x)=`\(x ^ 2 - 2 x -5 x^2 +3x ^3 -4x^4 +7 x ^2\)
`P(x)=(x^2-5x^2+7x^2)+3x^3-4x^4-2x`
`P(x)=3x^2+3x^3-4x^4-2x`
S.xếp: `P(x)=-4x^4+3x^3+3x^2-2x`
`c,`
Bậc của đa thức `P(x)` là bậc `4`
`d,`
Thay `x=0` vào đa thức `P(x)`
`P(0)=-4*0^4+3*0^3+3*0^2-2*0=0+0+0-0=0`
Vậy, `x=0` là nghiệm của đa thức.
Nếu là đa thức thì mình giúp được, nma kiểu c/minh nâng cao thì tớ k nghĩ là tớ đủ khả năng làm, vì dạo h tớ đang học chuyên anh để mai thi hsg nên k có tgian học nâng cao cho lắm:").
\(\dfrac{x-1}{2019-2}+\dfrac{x-3}{2019}=\dfrac{x-5}{2021}+\dfrac{x-7}{2023}\)
\(\Leftrightarrow\dfrac{x-1}{2017}+\dfrac{x-3}{2019}=\dfrac{x-5}{2021}+\dfrac{x-7}{2023}\)
\(\Leftrightarrow\left(\dfrac{x-1}{2017}+1\right)+\left(\dfrac{x-3}{2019}+1\right)=\left(\dfrac{x-5}{2021}+1\right)+\left(\dfrac{x-7}{2023}+1\right)\)
=>x+2016=0
hay x=-2016