x-1 / 2015 + x-3 / 2013 = x-5 / 2011 + x-7 / 2009
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NH
0
NH
0
1 tháng 4 2022
\(\dfrac{x-1}{2013}+\dfrac{x-2}{2012}+\dfrac{x-3}{2011}=\dfrac{x-4}{2010}+\dfrac{x-5}{2009}+\dfrac{x-6}{2008}\)
\(\Leftrightarrow\dfrac{x-1}{2013}-1+\dfrac{x-2}{2012}-1+\dfrac{x-3}{2011}-1=\dfrac{x-4}{2010}-1+\dfrac{x-5}{2009}-1+\dfrac{x-6}{2008}-1\)
=>x-2014=0
hay x=2014
TT
0
LN
1
L
22 tháng 1 2019
ta có pt trên <=> \(\frac{7-x}{2009}+1+\frac{5-x}{2011}+1+\frac{3-x}{2013}=0\)
<=> \(\frac{7-x}{2009}+\frac{2009}{2009}+\frac{5-x}{2011}+\frac{2011}{2011}+\frac{3-x}{2013}+\frac{2013}{2013}=0\)
<=> \(\frac{2016-x}{2009}+\frac{2016-x}{2011}+\frac{2016-x}{2013}=0\)
<=> \(\left(2016-x\right)\left(\frac{1}{2009}+\frac{1}{2011}+\frac{1}{2013}\right)=0\)
do \(\frac{1}{2009}+\frac{1}{2011}+\frac{1}{2013}\) >0
=> 2016-x=0
=> x=2016
Tìm x nha mấy bạn :<
\(\frac{x-1}{2015}+\frac{x-3}{2013}=\frac{x-5}{2011}+\frac{x-7}{2009}\)
=> \(\frac{x-1}{2015}-1+\frac{x-3}{2013}-1=\frac{x-5}{2011}-1+\frac{x-7}{2009}-1\)
=> \(\frac{x-2016}{2015}+\frac{x-2016}{2013}=\frac{x-2016}{2011}+\frac{x-2016}{2009}\)
=> \(\frac{x-2016}{2009}+\frac{x-2016}{2011}-\frac{x-2016}{2013}-\frac{x-2016}{2015}=0\)
=> \(\left(x-2016\right).\left(\frac{1}{2009}+\frac{1}{2011}-\frac{1}{2013}-\frac{1}{2015}\right)\)
Vì \(\frac{1}{2009}>\frac{1}{2013};\frac{1}{2011}>\frac{1}{2015}\)
=> \(\frac{1}{2009}+\frac{1}{2011}-\frac{1}{2013}-\frac{1}{2015}\ne0\)
=> \(x-2016=0\)
=> \(x=2016\)