x-2014/14-x-2015/15=0
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Với x = 2014 => x + 1 = 2015
Ta có :
\(f\left(x\right)=x^{17}-2015x^{16}+2015x^{15}-2015x^{14}+....+2015x-1\)
<=> \(f\left(x\right)=x^{17}-\left(x+1\right)x^{16}+\left(x+1\right)x^{15}-\left(x+1\right)x^{14}+....+\left(x+1\right)x-1\)
<=> \(f\left(x\right)=x-1\)
<=> \(f\left(2014\right)=2014-1=2013\)
![](https://rs.olm.vn/images/avt/0.png?1311)
thay x=2014 ta có:
\(f\left(x\right)=2014^{17}-2015.2014^{16}+2015.2014^{15}-2015.2014^{14}+...+2015.2014-1 \)
=2014^17 - (2014+1).2014^16 + (2014+1).2014^15 - (2014+1).2014^14 + ... + (2014+1).2014-1
=2014^17 - 2014^17 - 2014^16 + 2014^16 + 2014^15 - 2014^15 + 2014^14 + ...-2014^3 - 2014^2 + 2014^2 + 2014 -1
=2014-1=2013
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{14}{13}\) x \(\frac{15}{14}\) x \(\frac{16}{15}\) x ... x \(\frac{2014}{2013}\)x \(\frac{2015}{2014}\)
= \(\frac{14x15x16x...x2013x2014x2015}{13x14x15x16x...x2013x2014}\)
= 14 x 2015
=28210
![](https://rs.olm.vn/images/avt/0.png?1311)
Trả lời:
a, x . ( 2013 + 2014 + 2015 ) = 0
=> x = 0 : ( 2013 + 2014 + 2015 )
=> x = 0
Vậy x = 0
b, x . 125 = 10000
=> x = 10000 : 125
=> x = 80
Vậy x = 80
c, 697 : [ ( 15 . x + 364 ) : x ] = 17
=> ( 15 . x + 364 ) : x = 697 : 17
=> ( 15 . x + 364 ) : x = 41
=> 15 . x + 364 = 41 . x
=> 41 . x - 15 . x = 364
=> ( 41 - 15 ) . x = 364
=> 26 . x = 364
=> x = 364 : 26
=> x = 14
Vậy x = 14
![](https://rs.olm.vn/images/avt/0.png?1311)
a: =>\(\left(\dfrac{2x+1}{9}+1\right)+\left(\dfrac{2x+2}{8}+1\right)+...+\left(\dfrac{2x+9}{1}+1\right)=0\)
=>2x+10=0
=>x=-5
b: \(\Leftrightarrow\left(\dfrac{x-1}{2015}-1\right)+\left(\dfrac{x-2}{2014}-1\right)+...+\left(\dfrac{x-2014}{2}-1\right)+\left(x-2016\right)=0\)
=>x-2016=0
=>x=2016
![](https://rs.olm.vn/images/avt/0.png?1311)
Giải:
\(B=\left(5+10+15+...+2015\right)\times\left(20142014\times2015-20152015\times2014\right)\)
\(B=\left(5+10+15+...+2015\right)\times\left(10001\times2014\times2015-10001\times2015\times2014\right)\)
\(B=\left(5+10+15+...+2015\right)\times0\)
\(B=0\)
Chúc em học tốt!
B = (5+10+15+.........+2015) x (20142014 x 2015-20152015 x 2014)
B = (5+10+15+.........+2015) x ( 2014 x 1001 x 2015 - 2015 x 1001 x 2014 ] B = (5+10+15+.........+2015) x 0B = 0 nha![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a,|2x+2014| lớn hơn hoặc bằng 0
|x+2015| lớn hơn hoặc bằng 0
mà |2x+2014|+|x+2015|=0
=> |2x+2014|=0
x=-1007
|x+2015|=0
x=-2015 (vô lí)
=> x thuộc tập hp rỗng
\(\frac{x-2014}{14}-\frac{x-2015}{15}=0\)
<=> \(\frac{15\left(x-2014\right)}{14\cdot15}-\frac{14\left(x-2015\right)}{14\cdot15}=0\)
<=> \(15x-30210-14x+28210=0\)
<=> \(x-2000=0\)
<=> \(x=2000\)
Vậy nghiệm của phương trình là S = { 2000 }
x-(2014/14-2015/15)=0
x-200/21=0
x=0+200/21
x=200/21