Question

Tìm x biết :

a ) \(\left|x-2015\right|=\frac{1}{2}\)

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

Answer 1

a)Vì |x−2015|= 1/2 nên x-2015=-1/2 hoặc x-2015=1/2

Nếu x-2015=-1/2 thì

x=2015+(-1)/2

x=4029/2

Nếu x-2015=1/2 thì

x=2015+1/2

x=4031/2

Vậy x=4029/2

hoặc x=4031/2

 

Answer 2

b)

Nếu x>2016 thì |x−2015|=x-2015 ,|x−2016|=x-2016

Khi đó: |x−2015|+|x−2016|=2017

=>x-2015+x-2016=2017

=>2x-4031=2017

=>2x=6048=>x=3024(thỏa mãn x>2016)

Nếu 2015<x<2016 thì |x−2015|=x-2015,

|x−2016|=2016-x. khi đó

|x−2015|+|x−2016|=2017

=>x-2015+2016-x=2017

=>1=2017(vô lý loại)

Nếu x>2015 thì |x−2015|=2015-x,|x−2016|=2016-x

Khi đó:

|x−2015|+|x−2016|=2017

=>2015-x+2016-x=2017

=>4031-2x=2017

=>2x=2014=>x=1007(thỏa mãn x<2015)

Vậy x=1007 hoặc x=3024