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NP
0
1 tháng 1
1)
\(\dfrac{x-1}{2014}+\dfrac{x-2}{2013}+\dfrac{x-3}{2012}+...+\dfrac{x-2014}{1}=2014\)
\(\Leftrightarrow\left(\dfrac{x-1}{2014}-1\right)+\left(\dfrac{x-2}{2013}-1\right)+...+\left(\dfrac{x-2014}{1}-1\right)=0\)
\(\Leftrightarrow\dfrac{x-2015}{2014}+\dfrac{x-2015}{2013}+...+\dfrac{x-2015}{1}=0\)
\(\Leftrightarrow\left(x-2025\right)\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1}\right)=0\)
\(\Leftrightarrow x=2015\)
Vậy \(S=\left\{2015\right\}\)
NV
Nguyễn Việt Lâm
Giáo viên
14 tháng 4 2020
\(\Leftrightarrow\frac{2-x}{2012}+1=\frac{1-x}{2013}+1+1-\frac{x}{2014}\)
\(\Leftrightarrow\frac{2014-x}{2012}=\frac{2014-x}{2013}+\frac{2014-x}{2014}\)
\(\Leftrightarrow\left(2014-x\right)\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2012}\right)=0\)
\(\Leftrightarrow2014-x=0\Rightarrow x=2014\)
PN
0
LT
0
G
11 tháng 5 2023
\(\dfrac{x}{2012}+\dfrac{x+1}{2013}+\dfrac{x+2}{2014}+\dfrac{x+3}{2015}+\dfrac{x+4}{2016}=5\)
\(\Leftrightarrow\dfrac{x}{2012}+\dfrac{x+1}{2013}+\dfrac{x+2}{2014}+\dfrac{x+3}{2015}+\dfrac{x+4}{2016}-5=0\)
\(\Leftrightarrow\dfrac{x}{2012}-1+\dfrac{x+1}{2013}-1+\dfrac{x+2}{2014}-1+\dfrac{x+3}{2015}+\dfrac{x+4}{2016}-1=0\)
\(\Leftrightarrow\dfrac{x-2012}{2012}+\dfrac{x-2012}{2013}+\dfrac{x-2012}{2014}+\dfrac{x-2012}{2015}+\dfrac{x-2012}{2016}=0\)
\(\Leftrightarrow\left(x-12\right).\left(\dfrac{1}{2012}+\dfrac{1}{2013}+\dfrac{1}{2014}+\dfrac{1}{2015}+\dfrac{1}{2016}\right)=0\)
\(\Leftrightarrow x-12=0\)
\(\Leftrightarrow x=12\)
NC
1
5 tháng 9 2019
\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+\frac{x+4}{2011}=0\)
\(\Leftrightarrow\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)+\left(\frac{x+3}{2012}+1\right)+\left(\frac{x+4}{2011}+1\right)=0+1+1+1+1\)
\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}+\frac{x+2015}{2011}=4\)
\(\Leftrightarrow\left(x+2015\right).\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\right)=4\)
\(\Leftrightarrow x+2015=4:\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\right)\)
\(\Leftrightarrow x+2015=2012,499379\)
\(\Leftrightarrow x=2012,499379-2015\)
\(\Leftrightarrow x=-2,5006118\)
P/s : Số xấu quá !
\(\frac{1-x}{2013}=1+\frac{2-x}{2012}-\frac{x}{2014}\)
\(\Leftrightarrow\)\(\frac{1-x}{2013}+1=\frac{2-x}{2012}+1-\left(\frac{x}{2014}-1\right)\)
\(\Leftrightarrow\)\(\frac{2014-x}{2013}=\frac{2014-x}{2012}-\frac{x-2014}{2014}\)
\(\Leftrightarrow\)\(\frac{2014-x}{2013}-\frac{2014-x}{2012}+\frac{2014-x}{2014}\)=0
\(\Leftrightarrow\)(2014-x)(\(\frac{1}{2013}-\frac{1}{2012}+\frac{1}{2014}\))=0
\(\Leftrightarrow\)2014-x=0(do 1/2013 -1/2012 -1/2014)
\(\Leftrightarrow\)x=2014