mod(2x-[x])=4

where [] represent greatest integer function

 

Asked by hrishityelchuri2017 | 19th May, 2020, 09:58: AM

Expert Answer:

|2x-[x]|=4
2x-[x]=4    if  2x>[x]
2x-[x]=-4   if  2x<[x]
 
Take 2x<[x] which means [x]>2x
This is possible when -1
Therefore, 2x-[x]=-4 implies 2x-(-1)=-4 i.e. 2x=-4-1 i.e. x=-5/2=-2.5
Since, -1
Therefore, x=-2.5 is not possible.
 
Therefore, 2x-[x]=4    for  2x>[x]   
This is true for every x>0

Answered by Renu Varma | 21st May, 2020, 02:54: PM