(x+4)/2011+(x+3)/2012=(x+2)/2013+(x+1)/2014.tìm x
K
Khách
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DM
1
TT
4
10 tháng 4 2016
\(\frac{x+3}{2013}+1+\)\(\frac{x+4}{2012}+1+\frac{x+5}{2011}+1\)=\(\frac{x+1}{2015}+1+\frac{x+2}{2014}+1+\frac{x}{2016}+1\)
\(\Rightarrow\frac{x+2016}{2013}+\frac{x+2016}{2012}+\frac{x+2016}{2011}=\frac{x+2016}{2014}+\frac{x+2016}{2016}\)
\(\Rightarrow\left(2016+x\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2015}+\frac{1}{2014}+\frac{1}{2016}=0\right)\)
Vì 1/2016+...+1/2011>0 nên (x+2016)=0
suy ra x= -2016
nếu đúng xin kết bạn
ch
CM
0
PN
0
NN
2
15 tháng 8 2017
\(\frac{x+1}{2014}+\frac{x+2}{2013}=\frac{x+3}{2012}+\frac{x+4}{2011}\)
\(\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)=\left(\frac{x+3}{2012}+1\right)+\left(\frac{x+4}{2011}+1\right)\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}=\frac{x+2015}{2012}+\frac{x+2015}{2011}\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}-\frac{x+2015}{2012}-\frac{x+2015}{2011}=0\)
\(\left(x+2015\right).\left(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\right)=0\)
\(\Rightarrow\hept{\begin{cases}x+2015=0\\\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}=0\end{cases}}\)
Vì \(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\ne0\Rightarrow x+2015=0\Rightarrow x=-2015\)
Vậy x = 2015 nha bn
TN
15 tháng 8 2017
\(\frac{x+1}{2014}+\frac{x+2}{2013}=\frac{x+3}{2012}+\frac{x+4}{2011}\)
\(\Rightarrow\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)=\left(\frac{x+3}{2012}+1\right)+\left(\frac{x+4}{2011}+1\right)\)
\(\Rightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}=\frac{x+2015}{2012}+\frac{x+2015}{x+2011}\)
\(\Rightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}-\frac{x+2015}{2012}-\frac{x+2015}{2011}=0\)
\(\Rightarrow\left(x+2015\right).\left(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\right)\)
Vì \(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\ne0\Rightarrow\left(x-2015\right)=0\)
\(\Rightarrow x=0+2015\) =2015
Đúng thì k ủng hộ mik nha mn!
NK
0
7 tháng 1 2019
\(\dfrac{x-1}{2014}+\dfrac{x-2}{2013}=\dfrac{x-3}{2012}+\dfrac{x-4}{2011}\)
\(\Leftrightarrow\text{}\text{}\text{}\dfrac{x-1}{2014}-1+\dfrac{x-2}{2013}-1=\dfrac{x-3}{2012}-1+\dfrac{x-4}{2011}-1\)
\(\Leftrightarrow\dfrac{x-2015}{2014}+\dfrac{x-2015}{2013}-\dfrac{x-2015}{2012}-\dfrac{x-2015}{2011}=0\)
\(\Leftrightarrow\left(x-2015\right)\left(\dfrac{1}{2014}+\dfrac{1}{2013}-\dfrac{1}{2012}-\dfrac{1}{2011}\right)=0\)
mà \(\dfrac{1}{2014}+\dfrac{1}{2013}-\dfrac{1}{2012}-\dfrac{1}{2011}\ne0\)
nên \(x-2015=0\)
\(\Leftrightarrow x=2015\)
28 tháng 8 2016
x+1/2014 + x+2/2013 = x+3/2012 + x+4/2011
=> x+1/2014 + 1 + x+2/2013 + 1 = x+3/2012 + 1 + x+4/2011 + 1
=> x+2015/2014 + x+2015/2013 = x+2015/2012 + x+2015/2011
=> x+2015/2012 + x+2015/2011 - x+2015/2013 - x+2015/2014 = 0
=> (x + 2015).(1/2012 + 1/2011 - 1/2013 - 1/2014) = 0
Vì 1/2011 > 1/2013; 1/2012 > 1/2014
=> 1/2012 + 1/2011 - 1/2013 - 1/2014 khác 0
=> x + 2015 = 0
=> x = -2015
bấm vào chữ xanh này nha bn : /hoi-dap/question/113985.html