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NN
2 tháng 5 2019
\(\frac{x-1}{2018}+\frac{x-2}{2017}+\frac{x-3}{2016}+\frac{x-2043}{8}\)\(=0\)
\(\Leftrightarrow\)\(\frac{x-1}{2018}-1+\frac{x-2}{2017}-1+\frac{x-3}{2016}-1\)\(+\frac{x-2043}{8}+3=0\)
\(\Leftrightarrow\)\(\frac{x-1}{2018}-\frac{2018}{2018}+\frac{x-2}{2017}-\frac{2017}{2017}\)\(+\frac{x-3}{2016}-\frac{2016}{2016}+\frac{x-2043}{8}+\frac{24}{8}=0\)
\(\Leftrightarrow\)\(\frac{x-2019}{2018}+\frac{x-2019}{2017}+\frac{x-2019}{2016}\)\(+\frac{x-2019}{8}=0\)
\(\Leftrightarrow\)\(\left(x-2019\right).\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{8}\right)=0\)
\(\Leftrightarrow\)\(x-2019=0\) ( Vì \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{8}\ne0\))
\(\Leftrightarrow\) \(x=2019\)
Vậy phương trình có nghiệm là : \(x=2019\)
OM
5 tháng 4 2020
a, Làm
\(\frac{x+1}{2020}+\frac{x+2}{2019}+\frac{x+3}{2018}=\frac{x+4}{2017}+\frac{x+5}{2016}+\frac{x+6}{2015}\)
<=>\(\frac{x+2021}{2020}+\frac{x+2021}{2019}+\frac{x+2021}{2018}=\frac{x+2021}{2017}+\frac{x+2021}{2016}+\frac{x+2021}{2015}\)
<=>\(\left(x+2021\right)\left(\frac{1}{2020}+\frac{1}{2019}+\frac{1}{2018}-\frac{1}{2017}-\frac{1}{2016}-\frac{1}{2015}\right)=0\)
<=> x+2021=0
<=> x=-2021
Kl:......................
b, Làmmmmm
\(\frac{2-x}{2004}-1=\frac{1-x}{2005}-\frac{x}{2006}\)
<=> \(\frac{2006-x}{2004}=\frac{2006-x}{2005}+\frac{2006-x}{2006}\)
<=> \(\left(2006-x\right)\left(\frac{1}{2004}-\frac{1}{2005}-\frac{1}{2006}\right)=0< =>2006-x=0\)
<=> x=2006
Kl:..............
CE
4
23 tháng 3 2019
\(\frac{x-2}{2016}+\frac{x-3}{2017}+\frac{x-4}{2018}+3=0\\ \Leftrightarrow\left(\frac{x-2}{2016}+1\right)+\left(\frac{x-3}{2017}+1\right)+\left(\frac{x-4}{2018}+1\right)=0\\ \Leftrightarrow\frac{x+2014}{2016}+\frac{x+2014}{2017}+\frac{x+2014}{2018}=0\\ \Leftrightarrow\left(x+2014\right)\left(\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\right)=0\\ Vì\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\ne0\\ \Rightarrow x+2014=0\\ \Leftrightarrow x=-2014\\ Vậy...\)
28 tháng 2 2020
Ta có : \(\frac{x+2}{2018}+\frac{x+3}{2017}+\frac{x+4}{2016}+\frac{x+2038}{6}=0\)
=> \(\frac{x+2}{2018}+1+\frac{x+3}{2017}+1+\frac{x+4}{2016}+1+\frac{x+2038}{6}-3=0\)
=> \(\frac{x+2}{2018}+\frac{2018}{2018}+\frac{x+3}{2017}+\frac{2017}{2017}+\frac{x+4}{2016}+\frac{2016}{2016}+\frac{x+2038}{6}-\frac{18}{6}=0\)
=> \(\frac{x+2000}{2018}+\frac{x+2000}{2017}+\frac{x+2000}{2016}+\frac{x+2000}{6}=0\)
=> \(\left(x+2000\right)\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{6}\right)=0\)
=> \(x+2000=0\)
=> \(x=-2000\)
Vậy phương trình trên có tập nghiệm là \(S=\left\{-2000\right\}\)
1 tháng 5 2019
d, 2x2-5x-3 = 0
\(\Leftrightarrow\)2x2-6x+x-3= 0
\(\Leftrightarrow\)(2x2-6x) +(x-3) = 0
\(\Leftrightarrow\)2x(x-3) + (x-3) = 0
\(\Leftrightarrow\)(x-3) (2x+1) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\2x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\frac{-1}{2}\end{matrix}\right.\)
Vậy phương trình có tập nghiệm S =\(\left\{3;\frac{-1}{2}\right\}\)
26 tháng 3 2020
Ta có \(\frac{2015}{2016}.x+\frac{2016}{2017}.x+\frac{2017}{2018}.x=\frac{2018}{2019}.x\)
<=>\(\frac{2015}{2016}.x+\frac{2016}{2017}.x+\frac{2017}{2018}x-\frac{2018}{2019}x=0\)
<=>x\(\left(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}-\frac{2018}{2019}\right)=0\)
Vì \(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}-\frac{2018}{2019}\) không thể bằng 0
Vậy x=0
Ta có 1 nghiệm thỏa mãn S=\(\left\{0\right\}\)
13 tháng 1 2018
a, <=> (59-x/41 + 1) + (57-x/43 + 1) + (55-x/45 + 1) + (53-x/47 + 1) + (51-x/49 + 1) = 0
<=> 100-x/41 + 100-x/43 + 100-x/45 + 100-x/47 + 100-x/49 = 0
<=> (100-x).(1/41+1/43+1/45+1/47+1/49) = 0
<=> 100-x=0 ( vì 1/41+1/43+1/45+1/47+1/49 > 0 )
<=> x=100
Vậy x = 100
b, <=> 2-x/2016 + 1 = (1-x/2017 + 1) + (1 - x/2018)
<=> 2018-x/2016 = 2018-x/2017 + 2018-x/2018
<=> 2018-x/2016 - 2018-x/2017 - 2018-x/2018 = 0
<=> (2018-x).(1/2016-1/2017-1/2018) = 0
<=> 2018-x=0 ( vì 1/2016-1/2017-1/2018 khác 0 )
<=> x=2018
Vậy x=2018
Tk mk nha
1 tháng 4 2020
Giải các pt sau:
a) (x+4)(2x-3)=0
TH1: x+4=0 => x=-4
TH2 : 2x-3=0 => 2x=3 =>x=3/2
\(\Leftrightarrow\frac{x-3}{2016}-1=\left(\frac{x-2}{2017}-1\right)+\left(\frac{x-1}{2018}-1\right)\)
\(\Leftrightarrow\frac{x-3-2016}{2016}=\frac{x-2-2017}{2017}+\frac{x-1-2018}{2018}\)
\(\Leftrightarrow\frac{x-2019}{2016}-\frac{x-2019}{2017}-\frac{x-2019}{2018}=0\)
\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{2016}-\frac{1}{2017}-\frac{1}{2018}\right)=0\)
Vì \(\frac{1}{2016}-\frac{1}{2017}-\frac{1}{2018}\ne0\) ( không tin cứ bấm máy tính mà xem =)) )
\(\Rightarrow x-2019=0\Rightarrow x=2019\)