\(\frac{x}{2015}+\frac{x}{2016}=\frac{x}{2016}+\frac{x}{2017}\)

\(\Rightarrow\frac{x}{2015}+\frac{x}{2016}-\frac{x}{2016}-\frac{x}{2017}=0\)

\(\Rightarrow\frac{x}{2015}-\frac{x}{2017}=0\)

\(\Rightarrow x.\left(\frac{1}{2015}-\frac{1}{2017}\right)=0\)

Mà ta thấy \(\frac{1}{2015}-\frac{1}{2017}\ne0\Rightarrow x=0\)

Vậy \(x=0\)

\(\frac{x}{2015}+\frac{x}{2016}=\frac{x}{2016}+\frac{x}{2017}\)

\(\Leftrightarrow\frac{x}{2015}+\frac{x}{2016}-\frac{x}{2016}-\frac{x}{2017}=0\)

\(\Leftrightarrow x\left(\frac{1}{2015}+\frac{1}{2016}-\frac{1}{2016}-\frac{1}{2017}\right)=0\)

\(\Leftrightarrow x=0\).Do \(\frac{1}{2015}+\frac{1}{2016}-\frac{1}{2016}-\frac{1}{2017}\ne0\)

Vậy giá trị của x là x=0

\(\left|\frac{x}{2015}+\frac{x}{2016}\right|=\left|\frac{x}{2016}+\frac{x}{2017}\right|\)

<=>\(\left|x\right|.\left|\frac{1}{2015}+\frac{1}{2016}\right|=\left|x\right|.\left|\frac{1}{2016}+\frac{1}{2017}\right|\)

<=>\(\left|x\right|.\left(\frac{1}{2015}+\frac{1}{2016}\right)=\left|x\right|.\left(\frac{1}{2016}+\frac{1}{2017}\right)\)

<=>\(\left|x\right|.\left(\frac{1}{2015}+\frac{1}{2016}\right)-\left|x\right|.\left(\frac{1}{2016}+\frac{1}{2017}\right)=0\)

<=>\(\left|x\right|.\left(\frac{1}{2015}+\frac{1}{2016}-\frac{1}{2016}-\frac{1}{2017}\right)=0\)

<=>\(\left|x\right|.\left(\frac{1}{2015}-\frac{1}{2017}\right)=0\)

Vì \(\frac{1}{2015}-\frac{1}{2017}\ne0\Rightarrow\left|x\right|=0\Rightarrow x=0\)

Vậy x=0

\(\left|\frac{x}{2015}+\frac{x}{2016}\right|=\left|\frac{x}{2016}+\frac{x}{2017}\right|\)

\(\Rightarrow\left|x.\left(\frac{1}{2015}+\frac{1}{2016}\right)\right|=\left|x.\left(\frac{1}{2016}+\frac{1}{2017}\right)\right|\)

\(\Rightarrow\left|x\right|.\left|\frac{1}{2015}+\frac{1}{2016}\right|=\left|x\right|.\left|\frac{1}{2016}+\frac{1}{2017}\right|\)

\(\Rightarrow\left|x\right|.\left(\frac{1}{2015}+\frac{1}{2016}\right)=\left|x\right|.\left(\frac{1}{2016}+\frac{1}{2017}\right)\)

Mà \(\frac{1}{2015}+\frac{1}{2016}>\frac{1}{2016}+\frac{1}{2017}\)

=> |x| = 0

=> x = 0

Vậy x = 0

x = -2014

X = 2014 

ĐUNG

| x + 2015 | + 2016 = 2017 

| x + 2015 | = 2017 - 2016 = 1 

x + 2015 = 1 hoặc x + 2015 = -1 

x = 1 - 2015 hoặc x = -1 - 2015 

x = -2014 hoặc x = - 2016 

\(\frac{x}{2015}+\frac{x}{2016}=\frac{x}{2016}+\frac{x}{2017}\)

=>\(\frac{x}{2015}=\frac{x}{2017}\)

Vì 2015 khác 2017. Nên x=0

Do |x+2015| lớn hoặc = 0 với mọi x nên A bé hơn hoặc bằng -2016

Dấu "=" xảy ra khi và chỉ khi x+2015=0

=> x=-2015

|x+2015|+2016=2017

|x+2015|=2017-2016

|x+2015|=1

|x+2015|=+1

=>x+2015=1=>x=-2014

=>x+2015=-1=>x=-2016

Vay .....................

k mik nha ban

ta co:/x+2015/=2017-2016=1

{x+2015=1;x=-2014

x+2015=-1;x=-2016

theo đề bài: /x+2015/+2016=2017 (đkxđ: x c  Z)

=> /x+2015/=2017-2016=1

=> x+2015=1 hoặc x+2015=-1

giải hai bài toán ta được tập hợp xc { -2014; -2016}

\(A=\left|x-2015\right|+\left|x-2016\right|+\left|x-2017\right|+\left|x-2018\right|\)

\(=\left(\left|x-2015\right|+\left|2018-x\right|\right)+\left(\left|x-2016\right|+\left|2017-x\right|\right)\)

\(\ge\left|x-2015+2018-x\right|+\left|x-2016+2017-x\right|\)

\(=4\)

Dấu \(=\)khi \(2016\le x\le2017\).

Lời giải:

Tại $x=2016$ thì $x-2016=0$

Khi đó:
$A=x^{2016}(x-2016)-x^{2015}(x-2016)+x^{2014}(x-2016)-x^{2013}(x-2016)+.....-x(x-2016)+x-2017$

$=x^{2016}.0-x^{2015}.0+......-x.0+2016-2017=2016-2017=-1$