x-1/2021+x-2/2020=x-5/2017+x-7/2015
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S
2
17 tháng 3 2020
\(\frac{x-1}{2020}+\frac{x-2}{2021}=\frac{x+1}{2018}+\frac{x+2}{2017}\)
\(\Leftrightarrow\frac{x-1}{2020}+1+\frac{x-2}{2021}-1=\frac{x+1}{2018}+1+\frac{x+2}{2017}+1\)
\(\Leftrightarrow\frac{x+2019}{2020}+\frac{x+2019}{2021}=\frac{x+2019}{2018}+\frac{x+2019}{2017}\)
\(\Leftrightarrow\left(x+2019\right)\left(\frac{1}{2020}+\frac{1}{2021}-\frac{1}{2018}-\frac{1}{2017}\right)=0\)
mà \(\frac{1}{2020}+\frac{1}{2021}-\frac{1}{2018}-\frac{1}{2017}\ne0\)
\(\Leftrightarrow x+2019=0\)
\(\Leftrightarrow x=-2019\)
R
24 tháng 8 2019
Hello bạn, mk cx tên Mai nek.
\(\frac{2}{5}.\left(x-1\right)+1=\frac{3}{5}\)
\(\Rightarrow\frac{2}{5}\left(x+1\right)=\frac{3}{5}-1\)
\(\Rightarrow\frac{2}{5}\left(x+1\right)=-\frac{2}{5}\)
\(\Rightarrow x+1=-\frac{2}{5}:\frac{2}{5}\)
\(\Rightarrow x+1=-1\)
\(\Rightarrow x=-1-1\)
\(\Rightarrow x=-2\)
24 tháng 8 2019
\(\left(\frac{2}{7}\times x+1\right)\times\left(3-\frac{1}{2}\times x\right)=0\)
\(TH1:\frac{2}{7}\times x+1=0\)
\(\frac{2}{7}\times x=-1\)
\(x=-\frac{2}{7}\)
\(TH2:3-\frac{1}{2}\times x=0\)
\(\frac{1}{2}\times x=3\)
\(x=\frac{3}{2}\)
Vậy \(x\in\left\{\frac{3}{2};-\frac{2}{7}\right\}\)
TV
0
OY
1 tháng 8 2021
1/ \(\left(\dfrac{2021}{2020}+\dfrac{2020}{2021}\right).\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)
=\(\left(\dfrac{2021}{2020}+\dfrac{2020}{2021}\right).0\)
=\(0\)
KL
4 tháng 8 2017
a, \(\dfrac{2017.2021-4031}{2020+2017.2018}\)
= \(\dfrac{2017\left(2018+3\right)-4031}{2020+2017.2018}\)
= \(\dfrac{2017.2018+2017.3-4031}{2020+2017.2018}\)
= \(\dfrac{2017.2018+2020}{2020+2017.2018}\)
= 1
@Nguyen Thi Ngoc Linh
NT
0
K
1
KN
9 tháng 10 2020
Đặt \(2020-x=u;x-2021=v\)thì \(u+v=-1\)
Phương trình trở thành \(\frac{u^2+uv+v^2}{u^2-uv+v^2}=\frac{19}{49}\Leftrightarrow30u^2+30v^2+68uv=0\)
\(\Leftrightarrow15\left(u+v\right)^2+4uv=0\Leftrightarrow4uv=-15\Leftrightarrow uv=\frac{-15}{4}\)
hay \(\left(2020-x\right)\left(x-2021\right)=-\frac{15}{4}\Leftrightarrow x^2-4041x+4082416,25=0\)
Dùng công thức nghiệm tìm được x = 2022, 5 hoặc x = 2018, 5
14 tháng 3 2019
Ta có:\(\frac{3-x}{2021}+\frac{2020-x}{2019}+\frac{4033-x}{2017}+\frac{6042-x}{2015}=10\)
\(\Leftrightarrow\frac{3-x}{2021}-1+\frac{2020-x}{2019}-2+\frac{4033-x}{2017}-3+\frac{6042-x}{2015}-4=0\)
\(\Leftrightarrow\frac{3-x-2021}{2021}+\frac{2020-x-4038}{2019}+\frac{4033-x-6051}{2017}+\frac{6042-x-8060}{2015}=0\)
\(\Leftrightarrow\frac{-2018-x}{2021}+\frac{-2018-x}{2019}+\frac{-2018-x}{2017}+\frac{-2018-x}{2015}=0\)
\(\Leftrightarrow-\left(2018+x\right)\left(\frac{1}{2021}+\frac{1}{2019}+\frac{1}{2017}+\frac{1}{2015}\right)=0\)
\(\Leftrightarrow2018+x=0.Do\frac{1}{2021}+\frac{1}{2019}+\frac{1}{2017}+\frac{1}{2015}>0\)
\(\Leftrightarrow x=-2018\)
V...
\(\dfrac{x-1}{2021}+\dfrac{x-2}{2020}=\dfrac{x-5}{2017}+\dfrac{x-7}{2015}\\ \dfrac{x-1}{2021}+\dfrac{x-2}{2020}-2=\dfrac{x-5}{2017}+\dfrac{x-7}{2015}-2\\ \dfrac{x-1}{2021}+\dfrac{x-2}{2020}-1-1=\dfrac{x-5}{2017}+\dfrac{x-7}{2015}-1-1\\\left(\dfrac{x-1}{2021}-1\right)+\left(\dfrac{x-2}{2020}-1\right)=\left(\dfrac{x-5}{2017}-1\right)+\left(\dfrac{x-7}{2015}-1\right)\\ \dfrac{x-2022}{2021}+\dfrac{x-2022}{2020}=\dfrac{x-2022}{2017}+\dfrac{x-2022}{2015}\\ \dfrac{x-2022}{2021}+\dfrac{x-2022}{2020}-\dfrac{x-2022}{2017}-\dfrac{x-2022}{2015}=0\\ \left(x-2022\right)\left(\dfrac{1}{2021}+\dfrac{1}{2020}-\dfrac{1}{2017}-\dfrac{1}{2015}\right)=0\)
mà `(1/2021+1/2020-1/2017-1/2015 \ne 0`
nên `x-2022=0`
`x=2022`
hơi lấn cấn ở khúc 2 vế đều trừ 2 rồi xuống dòng lại trừ 1 trừ1