Question

the number of solutions of 4[x] = x + {x}, where [.] and {•} denote the greatest integer function and the fractional part function respectively is ??​

Answer 1

Step-by-step explanation:

We have,

$4 [x] = x + \{ x\}$

We know, any number can be written as sum of its integer part and fractional part, i.e., $\:n=[n]+\{n\}$, so,

$\implies \: 4 [x] =[x] + \{ x\} + \{ x\}$

$\implies \: 4 [x] - [x] = 2 \{ x\}$

$\implies \: 3[x] = 2 \{ x\}$

This is not possible, because

$\tt\:\green{fractional\:\: number\:\:is\:\:not\:\:equal\:\:to\:\:integer\:\:number}$

$\red{\sf{The\:\:no.\:\:of\:\:solutions\:\:=0}}$