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TN
25 tháng 5 2016
\(\left(\frac{x+2015}{2014}-1\right)+\left(\frac{x+2015}{2013}-1\right)+\left(\frac{x+2015}{2012}-1\right)=3\left(\frac{x+2015}{2011}-1\right)\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=\frac{3\left(x+2015\right)}{2011}\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}-\frac{x+2015}{2011}+\frac{x+2015}{2011}+\frac{x+2015}{2011}=0\)
\(\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}+\frac{1}{2011}+\frac{1}{2011}\right)=0\)
\(x+2015=0\text{ Vì }\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}+\frac{1}{2011}+\frac{1}{2011}\ne0\)
\(x=-2015\)
30 tháng 4 2018
(1 - \(\dfrac{1}{2}\)) . (1 - \(\dfrac{1}{3}\)) . (1 - \(\dfrac{1}{4}\)) ... (1 - \(\dfrac{1}{x}\)) = \(\dfrac{1}{2014}\)
=> \(\dfrac{1}{2}\) . \(\dfrac{2}{3}\) . \(\dfrac{3}{4}\) ... \(\dfrac{x-1}{x}\) =\(\dfrac{1}{2014}\)
=> \(\dfrac{1.2.3...x-1}{2.3.4...x}\) = \(\dfrac{1}{2014}\)
=:> \(\dfrac{1}{x}\) = \(\dfrac{1}{2014}\)
Vậy x = 2014
(Mình nghĩa là vậy, có gì sai mong bạn bỏ qua nha)
MT
18 tháng 6 2015
\(\frac{x+4}{2011}+\frac{x+3}{2012}=\frac{x+2}{2013}+\frac{x+1}{2014}\)
\(\frac{x+4}{2011}+1+\frac{x+3}{2012}+1=\frac{x+2}{2013}+1+\frac{x+1}{2014}+1\)
\(\frac{x+4}{2011}+\frac{2011}{2011}+\frac{x+3}{2012}+\frac{2012}{2012}=\frac{x+2}{2013}+\frac{2013}{2013}+\frac{x+1}{2014}+\frac{2014}{2014}\)
\(\frac{x+2015}{2011}+\frac{x+2015}{2012}=\frac{x+2015}{2013}+\frac{x+2015}{2014}\)
\(\frac{x+2015}{2011}+\frac{x+2015}{2012}-\frac{x+2015}{2013}-\frac{x+2015}{2014}=0\)
\(\left(x+2015\right)\left(\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)=0\)
vì \(\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\ne0\)nên:
x+2015=0
x=-2015
KL
Tìm x \(\in\) Z biết:
1) \(\dfrac{1-x}{2017}+\dfrac{2-x}{2016}=\dfrac{3-x}{2015}+\dfrac{4-x}{2014}\)
1
15 tháng 8 2017
\(\dfrac{1-x}{2017}+\dfrac{2-x}{2016}=\dfrac{3-x}{2015}+\dfrac{4-x}{2014}\)
\(\left(\dfrac{1-x}{2017}+1\right)+\left(\dfrac{2-x}{2016}+1\right)=\left(\dfrac{3-x}{2015}+1\right)+\left(\dfrac{4-x}{2014}+1\right)\)
\(\dfrac{2018-x}{2017}+\dfrac{2018-x}{2016}=\dfrac{2018-x}{2015}+\dfrac{2018-x}{2014}\)
\(\Leftrightarrow\dfrac{2018-x}{2017}+\dfrac{2018-x}{2016}-\dfrac{2018-x}{2015}-\dfrac{2018-x}{2014}=0\)
\(\Leftrightarrow\left(2018-x\right)\left(\dfrac{1}{2017}+\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}\right)=0\)
Mà \(\left(\dfrac{1}{2017}+\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}\right)\ne0\)
\(\Leftrightarrow2018-x=0\Leftrightarrow x=2018\)
Vậy ...
20 tháng 7 2017
\(\dfrac{x+1}{2014}+\dfrac{x+2}{2013}+.....+\dfrac{x+1007}{1008}=\dfrac{x+1008}{1007}+\dfrac{x+1009}{1006}+........+\dfrac{x+2014}{1}\)\(\Leftrightarrow\left(\dfrac{x+1}{2014}+1\right)+\left(\dfrac{x+2}{2013}+1\right)+...+\left(\dfrac{x+1007}{1008}+1\right)=\left(\dfrac{x+1008}{1007}+1\right)+\left(\dfrac{x+1009}{1006}+1\right)+...+\left(\dfrac{x+2014}{1}+1\right)\)\(\Leftrightarrow\dfrac{x+2015}{2014}+\dfrac{x+2015}{2013}+...+\dfrac{x+1007}{1008}=\dfrac{x+2015}{1007}+\dfrac{x+1009}{1006}+...+\dfrac{x+2014}{1}\)\(\Leftrightarrow\dfrac{x+2015}{2014}+\dfrac{x+2015}{2013}+...+\dfrac{x+2015}{1008}-\dfrac{x+1008}{1007}-\dfrac{x+2015}{1006}-...-\dfrac{x+2015}{1}=0\)\(\Leftrightarrow\left(x+2015\right)\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1008}-\dfrac{1}{1007}-\dfrac{1}{1006}-...-1\right)=0\)\(\Leftrightarrow x+2015=0\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1008}-\dfrac{1}{1007}-\dfrac{1}{1006}-...-1>0\right)\)\(\Leftrightarrow x=-2015\)
Vậy x=-2015
15 tháng 8 2017
\(\dfrac{1-x}{2017}+\dfrac{2-x}{2016}=\dfrac{3-x}{2015}+\dfrac{4-x}{2014}\)
\(\Leftrightarrow\left(\dfrac{1-x}{2017}+1\right)+\left(\dfrac{2-x}{2016}+1\right)=\left(\dfrac{3-x}{2015}+1\right)+\left(\dfrac{4-x}{2014}+1\right)\)
\(\Leftrightarrow\dfrac{2018-x}{2017}+\dfrac{2018-x}{2016}=\dfrac{2018-x}{2015}+\dfrac{2018-x}{2014}\)
\(\Leftrightarrow\dfrac{2018-x}{2017}+\dfrac{2018-x}{2016}-\dfrac{2018-x}{2015}-\dfrac{2018-x}{2014}=0\)
\(\Leftrightarrow\left(2018-x\right)\left(\dfrac{1}{2017}+\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}\right)=0\)
Mà \(\dfrac{1}{2017}+\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}\ne0\)
\(\Leftrightarrow2018-x=0\Leftrightarrow x=2018\)
Vậy ....
M
2
TV
21 tháng 9 2015
4x+1 + 4x = 320 x 1
4 x 4x + 4x = 320
4x x 5 = 320
4x = 320 : 5
4x = 64
4x = 43
=> x = 3
17 tháng 2 2016
1.a) 113 + x chia hết cho 7
=> 112 + 1 + x chia hết cho 7
Mà 112 chia hết cho 7
=> 1 + x chia hết cho 7 ( hay x chia 7 dư 6 )
b) 113 + x chia hết cho 13
=> 104 + 9 + x chia hết cho 13
Mà 104 chia hết cho 13
=> x + 9 chia hết cho 13 ( hay x chia 13 dư 4 )
17 tháng 2 2016
a,x là B(6) nhưng khác 0
b,x là B(4) nhưng cũng khác 0
Chúc bạn học giỏi
\(\dfrac{1}{2}x+150\%x=2014\)
\(\Rightarrow\dfrac{1}{2}x+\dfrac{150}{100}x=2014\)
\(\Rightarrow\dfrac{1}{2}x+\dfrac{3}{2}x=2014\)
\(\Rightarrow x.\left(\dfrac{1}{2}+\dfrac{3}{2}\right)=2014\)
\(\Rightarrow2x=2014\)
\(\Rightarrow x=1007\)