Question

2[x]=x+{x} find the value of x ; where [.] is greatest integer function and {.} is fractional part function

Answer 1

Answer:

-1.5, 0.0

Step-by-step explanation:

Let the number x be divided into two parts.

integer part A, and fractional part b.

hence, X = A.b

case (b is not 0)

since b is not 0, therefore [X]=[A.b]= A+1

and {X}=0.b

then equation stands as

2(A+1)=A.b + 0.b,

2A +2= A + 2(0.b)

A=2(0.b)-2

now A is integer, 2 is also integer. hence, 2(0.b) should also be an integer.

if b is not zero and 0.b<=1, thus, 0.b=1/2=0.5

or, A=2(0.5)-2=-1

this, number is -1.5 (satisfies the equation)

case( b is 0)

since b is 0, [A.b]=A

thus, according to equation, 2A=A+0, which is possible off A=0. thus, the number is 0.0