Question

|x-2016|-|x-2017|=1

Answer 1

x = { -2017; -2016; 2016;2017 }

Answer 2

x={-2017;-2016;2016;2017}

Answer 3

\(\left|x-2016\right|-\left|x-2017\right|=1\)

TH1: \(x< 2016\)

<=>\(-x+2016-x+2017=1\)<=>\(-2x+4033=1\)

<=>\(-2x=-4032\)<=>\(x=2016\) (loại)

TH2: \(2016\le x\le2017\)

<=>\(x-2016-x+2017=1\)<=>\(1=1\) luôn đúng!

TH3: \(x>2017\)

<=>\(x-2016+x-2017=1\)<=>\(2x-4033=1\)

<=>\(2x=4034\)<=>\(x=2017\) (loại)

Vậy \(2016\le x\le2017\)

Answer 4

sorry, làm lại:

TH1: x<2016

<=> \(\left[-\left(x-2016\right)\right]-\left[-\left(x-2017\right)\right]=1\) 

<=>\(-x+2016+x-2017=1\)

<=>\(-1=1\) (loại)

TH2: \(2016\le x< 2017\)

<=>\(\left(x-2016\right)-\left[-\left(x-2017\right)\right]=1\)<=>\(x-2016+x-2017=1\)

<=>\(2x-4033=1\)<=>\(2x=4034\)<=>\(x=2017\) (loại)

TH3: \(x\ge2017\)

<=>\(\left(x-2016\right)-\left(x-2017\right)=1\)

<=>\(x-2016-x+2017=1\)

<=>\(1=1\) luôn đúng!

Vậy \(x\ge2017\)