Tim x, biet: \(\frac{x-2011}{12}+\frac{x-2011}{20}+\frac{x-2011}{30}+\frac{x-2011}{42}+\frac{x-2011}{56}+\frac{x-2011}{72}=\frac{16}{9}\)
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NV
0
T
17 tháng 9 2018
a) \(\frac{x+4}{2009}+1+\frac{x+3}{2010}+1=\frac{x+2}{2011}+1+\frac{x+1}{2012}\)
\(\frac{x+4+2009}{2009}+\frac{x+3+2010}{2010}=\frac{x+2+2011}{2011}+\frac{x+2+2012}{2012}\)
\(\frac{x+2013}{2009}+\frac{x+2013}{2010}-\frac{x+2013}{2011}-\frac{x+2013}{2012}=0\)
\(\left(x+2013\right).\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)=0\) (1)
Vì \(\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)\ne0\)
Nên biểu thức (1) xảy ra khi \(x+2013=0\)
\(x=-2013\)
b) \(\left(x-2011\right)\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)=0\) (2)
Vì \(\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)\ne0\)
Nên biểu thức (2) xảy ra khi \(x-2011=0\)
\(x=2011\)
PG
1
14 tháng 6 2017
ta co (x-2163)(1/2011+1/28+1/124)=0
vi 1/2011+1/28+1/124khac0
x-2163=0
x=2163
NN
0
NT
2
CW
1 tháng 1 2017
\(\frac{x-3}{2013}+\frac{x-4}{2012}=\frac{x-5}{2011}+\frac{x-6}{2010}\)
\(\Leftrightarrow\frac{x-3-2013}{2013}+\frac{x-2-2012}{2012}=\frac{x-5-2011}{2011}+\frac{x-6-2010}{2010}\)(mỗi vế trừ đi 2)
\(\Leftrightarrow\frac{x-2016}{2013}+\frac{x-2016}{2012}-\frac{x-2016}{2011}-\frac{x-2016}{2010}=0\)
\(\Leftrightarrow\left(x-2016\right)\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)
Mà \(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\ne0\)
\(\Rightarrow x-2016=0\Leftrightarrow x=2016\)
TC
5 tháng 10 2019
Cộng mỗi vế cho 1
Ta có: \(\frac{x-3-2013}{2013}+\frac{x-4-2012}{2012}=\frac{x-5-2011}{2011}+\frac{x-6-2010}{2010}\)
\(=>\left(\frac{x-2016}{2013}+\frac{x-2016}{2012}\right)-\left(\frac{x-2016}{2011}+\frac{x-2016}{2010}\right)=0\)
\(=>\left(x-2016\right).\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}\right)\)
Mà \(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}\ne0\)
\(=>x-2016=0\\ =>x=2016\)
TH
2
\(\left(x-2011\right)\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\cdot\frac{2}{9}=\frac{16}{9}\)
\(x-2011=8\)
\(x=2019\)
\(\frac{x-2011}{12}+\frac{x-2011}{20}+\frac{x-2011}{30}+\frac{x-2011}{42}+\frac{x-2011}{56}+\frac{x-2011}{72}=\frac{16}{9}\)
\(\left(x-2011\right)\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\frac{2}{9}=\frac{16}{9}\)
\(x-2011=8\Rightarrow x=2019\)