giải phương trình
(2-x)/2013-1=(1-x)/2014-x/2015
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KE
2
8 tháng 3 2018
pt <=> (x/2012 - 1) + (x+1/2013 - 1) + (x+2/2014 - 1) + (x+3/2015 - 1) + (x+4/2016 - 1) = 0
<=> x-2012/2012 + x-2012/2013 + x-2012/2014 + x-2012/2015 + x-2012/2016 = 0
<=> (x-2012).(1/2012+1/2013+1/2014+1/2015+1/2016) = 0
<=> x-2012 = 0 ( vì 1/2012+1/2013+1/2014+1/2015+1/2016 > 0 )
<=> x=2012
Vậy x=2012
Tk mk nha
8 tháng 3 2018
Ta có :
\(\frac{x}{2012}+\frac{x+1}{2013}+\frac{x+2}{2014}+\frac{x+3}{2015}+\frac{x+4}{2016}=5\)
\(\Leftrightarrow\)\(\left(\frac{x}{2012}-1\right)+\left(\frac{x+1}{2013}-1\right)+\left(\frac{x+2}{2014}-1\right)+\left(\frac{x+3}{2015}-1\right)+\left(\frac{x+4}{2016}-1\right)=5-5\)
\(\Leftrightarrow\)\(\frac{x-2012}{2012}+\frac{x-2012}{2013}+\frac{x-2012}{2014}+\frac{x-2012}{2015}+\frac{x-2012}{2016}=0\)
\(\Leftrightarrow\)\(\left(x-2012\right)\left(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}\right)=0\)
Vì \(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}\ne0\)
\(\Rightarrow\)\(x-2012=0\)
\(\Rightarrow\)\(x=2012\)
Vậy \(x=2012\)
Chúc bạn học tốt ~
PH
2
7 tháng 2 2020
(x-1)/2015 + x/2014 + 1/503 - (x-3)/2013 - x/2012 - 1/1007 =0
(x-2016)/2015 + (x-2016)/2014 - (x-2016)/2012 - (x-2016)/2013 = 0
(x-2016) ( 1/2015 + 1/2016 - 1/2013 - 1/2012) = 0
Mà 1/2015 + 1/2016 - 1/2013 - 1/2012 khác 0
Suy ra x -2016=0
x=2016
Chỗ nào thắc mắc nhớ hỏi mik nhe!
11 tháng 1 2017
Theo bài ra , ta có :
\(\frac{x+2}{2014}+\frac{x+1}{2015}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
\(\Leftrightarrow\left(\frac{x+2}{2014}+1\right)+\left(\frac{x+1}{2015}+1\right)=\left(\frac{x+3}{2013}+1\right)+\left(\frac{x+4}{2012}+1\right)\)
\(\Leftrightarrow\left(\frac{x+2+2014}{2014}\right)+\left(\frac{x+1+2015}{2015}\right)=\left(\frac{x+3+2013}{2013}\right)+\left(\frac{x+4+2012}{2012}\right)\)
\(\Leftrightarrow\frac{x+2016}{2014}+\frac{x+2016}{2015}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\)
\(\Leftrightarrow\frac{x+2016}{2014}+\frac{x+2016}{2015}-\frac{x+2016}{2013}-\frac{x+2016}{2012}=0\)
\(\Leftrightarrow\left(x+2016\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)
Vì \(\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2013}-\frac{1}{2012}\right)>0\)
\(\Leftrightarrow x+2016=0\)
\(\Leftrightarrow x=-2016\)
Vậy \(x=-2016\)
Tập nghiệm của phương trình là \(S=\left\{-2016\right\}\)
Chúc bạn học tốt =))
11 tháng 1 2017
\(\frac{x+2}{2014}+\frac{x+1}{2015}=\frac{x+3}{2013}+\frac{x+4}{2012}\)
\(\frac{x+2}{2014}+1+\frac{x+1}{2015}+1=\frac{x+3}{2013}+1+\frac{x+4}{2012}+1\)
\(\frac{x+2+2014}{2014}+\frac{x+1+2015}{2015}=\frac{x+3+2013}{2013}+\frac{x+4+2012}{2012}\)
\(\frac{x+2016}{2014}+\frac{x+2016}{2015}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\)
\(\frac{x+2016}{2014}+\frac{x+2016}{2015}-\frac{x+2016}{2013}-\frac{x+2016}{2012}=0\)
\(\left(x+2016\right).\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)
MÀ \(\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2013}-\frac{1}{2012}\right)\ne0\)
\(\Rightarrow x+2016=0\)
\(\Rightarrow x=-2016\)
26 tháng 2 2016
\(\frac{x+1}{2015}+\frac{x+2}{2014}=\frac{x+3}{2013}+\frac{x+4}{2012}\) <=> \(\frac{x+1}{2015}+1+\frac{x+2}{2014}+1=\frac{x+3}{2013}+1+\frac{x+4}{2012}+1\) <=> \(\frac{x+2016}{2015}+\frac{x+2016}{2014}=\frac{x+2016}{2013}+\frac{x+2016}{2012}\) <=> \(\frac{x+2016}{2015}+\frac{x+2016}{2014}-\frac{x+2016}{2013}-\frac{x+2016}{2012}=0\) <=> \(x+2016\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\) <=> x + 2016 = 0 <=> x = -2016
1 tháng 2 2019
(\dfrac{2-x}{2013}-1=\dfrac{1-x}{2014}-\dfrac{x}{2015}\)
\(\Leftrightarrow\dfrac{2-x+2013}{2013}-1+1=\dfrac{1-x+2014}{2014}+\dfrac{-x+2015}{2015}\) (Cộng 2 vế cho 1+1)
\(\Leftrightarrow\dfrac{2015-x}{2013}=\dfrac{2015-x}{2014}+\dfrac{2015-x}{2015}\)
\(\Leftrightarrow\dfrac{2015-x}{2013}-\dfrac{2015-x}{2014}-\dfrac{2015-x}{2015}=0\)
\(\Leftrightarrow\left(2015-x\right)\left(\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\right)=0\)
\(\Leftrightarrow2015-x=0\) (Vì \(\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\ne0\))
\(\Leftrightarrow x=2015\)
Vậy phương trình có tập nghiệm là x = 2015
1 tháng 2 2019
\(\dfrac{2-x}{2013}-1=\dfrac{1-x}{2014}-\dfrac{x}{2015}\)
\(\Leftrightarrow\dfrac{2-x+2013}{2013}-1+1=\dfrac{1-x+2014}{2014}+\dfrac{-x+2015}{2015}\) (Cộng 2 vế cho 1+1)
\(\Leftrightarrow\dfrac{2015-x}{2013}=\dfrac{2015-x}{2014}+\dfrac{2015-x}{2015}\)
\(\Leftrightarrow\dfrac{2015-x}{2013}-\dfrac{2015-x}{2014}-\dfrac{2015-x}{2015}=0\)
\(\Leftrightarrow\left(2015-x\right)\left(\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\right)=0\)
\(\Leftrightarrow2015-x=0\) (Vì \(\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\ne0\))
\(\Leftrightarrow x=2015\)
Vậy phương trình có tập nghiệm là x = 2015
30 tháng 11 2015
1).x:2+x:3=5/2
=>x.1/2+x.1/3=5/2
=>x(1/2+1/3)=5/2
=>x.5/6=5/2
=>x=5/2:5/6
=>x=3
\(\dfrac{2-x}{2013}-1=\dfrac{1-x}{2014}-\dfrac{x}{2015}\)
\(\Leftrightarrow\dfrac{2-x+2013}{2013}-1+1=\dfrac{1-x+2014}{2014}+\dfrac{-x+2015}{2015}\) (Cộng 2 vế cho 1+1)
\(\Leftrightarrow\dfrac{2015-x}{2013}=\dfrac{2015-x}{2014}+\dfrac{2015-x}{2015}\)
\(\Leftrightarrow\dfrac{2015-x}{2013}-\dfrac{2015-x}{2014}-\dfrac{2015-x}{2015}=0\)
\(\Leftrightarrow\left(2015-x\right)\left(\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\right)=0\)
\(\Leftrightarrow2015-x=0\) (Vì \(\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\ne0\))
\(\Leftrightarrow x=2015\)
Vậy phương trình có tập nghiệm là x = 2015