Home
Class 12
MATHS
If f(x) and [x] denote respectively the ...

If f(x) and [x] denote respectively the fractional and integeral parts of a real number x, then the number of solution of the euation 4{x}=x+[x] , is

Text Solution

Verified by Experts

`:'x=[x]+{x}` ……i
Then given equation reduces to
`4{x}=[x]+{x}|[x]`
`implies{x}=2/3[x]`…….ii
`:'0le{x}lt1=0le2/3[x]lt1` or `0le[x]lt3/2`
`:.[x]=0,1`
From Eq. iii `{x}=0,2/3`
From Eq. (i) `x=0,1+2/3` i.e. `x=0,5/3`
Promotional Banner

Similar Questions

Explore conceptually related problems

number of solution of the equation |x| = cos x

The number of real solution of the equation e^(x)+x=0, is

The number of real solution of the equation x^(2)=1-|x-5| is

The number of real solutions of the equation log_(0.5)x=|x| is

Find the number of solutions of 4{x}=x+[x].

The number of real solutions of the equation sin(e^x)=2^x+2^(-x) is

Let {x} and [x] denotes the fraction fractional and integral part of a real number (x) , respectively. Solve |2x-1|=3[x]+2{x} .

The number of real solution of equation Sin(e^x) = 5^x + 5^(-x) is :

The number of real solutions of the equation log_(a)x=|x|,0 lt a lt 1 , is

If [x] is the integral part of a real number x . Then solve [2x]-[x+1]=2x