Home
Class 12
MATHS
If [x] is the integral part of a real nu...

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

Text Solution

Verified by Experts

The correct Answer is:
`x_(1)=-1,x_(2)=-1//2`
We have `[2x]-[x+1]=2x`
Since LHS`=` Integer
`:.` RHS `=2x=` Integer
`implies[2x]=2x`
Now `-[x+1]=0`
`implies[x+1]=0`
or `0lex+1lt1`
or `-1lexlt0`
or `-2xle2xlt0`
`:.2x=-2,-1`
or `x=-1, -1/2`
or `x_(1)=-1,x_(2)=-1/2`
Promotional Banner

Similar Questions

Explore conceptually related problems

If [x] and (x) are the integral part of x and nearest integer to x then solve (x)[x]=1

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

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

If {x} and [x] represent fractiona and integral part of x respectively then solve the equation x-1=(x-[x])(x-{x})

Find the integration of the 1/(2x+1) .

a gt 1 is a real number f(x) = log_(a)x^2 , where x gt 0 If f^(-1)(x) is a inverse of f(x) and b and c are real numbers then f^(-1) (b+c) = ......

Solve 3x+8 gt2 , when (i) x is an integer. (ii) x is a real number.

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

How many real solutions of the equation 6x^(2)-77[x]+147=0 , where [x] is the integral part of x ?

Let f and g be real functions defined by f(x)= 2x + 1 and g(x)= 4x- 7 . For what real numbers x, f(x) lt g(x) ?