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TN
3
7 tháng 9 2015
(x + 4)/2010 + (x+3)/2011 = (x+2)/2012 + (x+1)/2013
<=> [(x + 4)/2010 + 1] + [(x+3)/2011 + 1] = [(x+2)/2012 + 1] + [(x+1)/2013 + 1]
<=> (x + 2014)/2010 + (x + 2014)/2011 = (x + 2014)/2012 + (x + 2014)/2013
<=> (x + 2014)/2010 + (x + 2014)/2011 - (x + 2014)/2012 - (x + 2014)/2013 = 0
<=> (x + 2014).(1/2010 + 1/2011 - 1/2012 - 1/2013) = 0
Ta thấy (1/2010 + 1/2011 - 1/2012 - 1/2013) ≠ 0
Vậy suy ra x = -2014
HT
1
9 tháng 8 2018
\(\frac{x-1}{2013}+\frac{x-2}{2012}-\frac{x-3}{2011}=\frac{x-4}{2010}\)
\(\frac{x-1}{2013}+\frac{x-2}{2012}-\frac{x-3}{2011}-\frac{x-4}{2010}=0\)
\(\frac{x-1}{2013}-1+\frac{x-2}{2012}-1-\frac{x-3}{2011}+1-\frac{x-4}{2010}+1=0\)
\(\left(\frac{x-1}{2013}-1\right)+\left(\frac{x-2}{2012}-1\right)-\left(\frac{x-3}{2011}-1\right)-\left(\frac{x-4}{2010}-1\right)=0\)
\(\frac{x-2014}{2013}+\frac{x-2014}{2012}-\frac{x-2014}{2011}-\frac{x-2014}{2010}=0\)
\(\left(x-2014\right).\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)
\(x-2014=0:\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)\)
\(x-2014=0\)
\(x=2014\)
Nhớ tk cho mình nha =3
A.R.M.Y FIGHTING!!!!
NT
1
23 tháng 2 2017
trước tiên bạn phải tính:
2013/1+2012/2+2011/3+.....+2/2012+1/2013
=1+2012/2)+(1+2011/3)+.....+(1+2/2012)+(1+1/2013) +1 {BƯỚC NÀY TÁCH 2013 RA LÀM 2013SỐ1 ĐỂ CÔNG VS CÁC THỪA SỐ CÒN LẠI}
=2014/2+2014/3+...+2014/2012+2014/2013+2014/2014
=2014.(1/2+1/3+....+1/2012+1/20131/2014
suy ra x=2014
S
2
HT
22 tháng 6 2016
Ta có : \(\frac{x+1}{2013}+\frac{x+2}{2012}+\frac{x+3}{2011}=-3.\)
\(\Leftrightarrow\frac{x+1}{2013}+1+\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=-3+3\)
\(\Leftrightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}=0\)
\(\Leftrightarrow\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\right)=0\)
Mà \(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\ne0\) nên \(x+2014=0\Leftrightarrow x=-2014\)
Vây \(x=-2014\)
NK
0
AD
1
NT
1
28 tháng 1 2018
\(\text{Đầu bài viết khó nhìn thí mồ!! viết lại nhé!!}\)
\(\frac{x+1}{2013}+\frac{x+2}{2012}+\frac{x+3}{2011}=\frac{x-1}{2015}+\frac{x-2}{2016}+\frac{x-3}{2017}\)
\(\Rightarrow\frac{x+1}{2013}+1+\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=\frac{x-1}{2015}+1+\frac{x-2}{2016}+1+\frac{x-3}{2017}+1\)
\(\Leftrightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}-\frac{x+2014}{2015}-\frac{x+2014}{2016}-\frac{x+2014}{2017}=0\)
\(\Leftrightarrow\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\right)=0\)
\(\text{Mà }\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\ne0\)
\(\text{Nên }x+2014=0\Leftrightarrow x=-2014\)
N
2
T
2 tháng 1 2017
\(\frac{x+1}{2013}+\frac{x+2}{2012}=\frac{x+3}{2011}+\frac{x+4}{2010}\)
\(\Rightarrow\left(\frac{x+1}{2013}+1\right)+\left(\frac{x+2}{2012}+1\right)=\left(\frac{x+3}{2011}+1\right)+\left(\frac{x+4}{2010}+1\right)\)
\(\Rightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}-\frac{x+2014}{2011}-\frac{x+2014}{2010}=0\)
\(\Rightarrow\left(x+2014\right).\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)
Vì \(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\ne0\)nên để \(\left(x+2014\right).\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)
Thì x+2014=0
=>x=-2014
2 tháng 1 2017
\(\frac{x+1}{2013}+\frac{x+2}{2012}=\frac{x+3}{2011}+\frac{x+4}{2010}\)
=> \(\frac{x+1+2013}{2013}+\frac{x+2+2012}{2012}=\frac{x+3+2011}{2011}+\frac{x+4+2010}{2010}\)
=> \(\frac{x+2014}{2013}+\frac{x+2014}{2012}=\frac{x+2014}{2011}+\frac{x+2014}{2010}\)
=> \(\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)
=> \(x+2014=0\)(do \(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\ne0\))
=> \(x=-2014\)
\(\frac{x+1}{2013}+\frac{x+2}{2012}+\frac{x+3}{2011}=-3\)
\(=>\frac{x+1}{2013}+\frac{x+2}{2012}+\frac{x+3}{2011}+3=0\)
\(=>\frac{x+1}{2013}+1+\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=0\)
\(=>\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}=0\)
\(=>\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\right)=0\)
=>x+2014=0 (vì \(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\) khác 0)
=>x=-2014