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

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

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

Solve the Inequality for real value x: 3(x-1) le 2 (x-3)

The set of all real numbers x for which x^(2)-|x+2|+x>0 is

Solve 5x-3 lt 7" when " , x is real number

The function f and g are given by : f(x)=(x) , the fractional part of x and g(x)=(1)/(2)sin[x]pi , where [x] denotes the integral part of x, then range of gof is :

Solve: 2x^(2) + x+1=0

Let f(x) = x - [x] , for every real number x, where [x] is integral part of x. Then int_(-1)^(1) f(x) dx is: