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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
Question
Solve the following for $x$, where $|x|$ is modulus function, $[x]$ is the greatest integer function, $\{x\}$ is a fractional part function.$2\{x\}=x+[x]$
✓

Answer

$ 2\{x\}=x+[x]$
$=[x]+\{x\}+[x] \ldots . .[x=[x]+\{x\}]$
$\therefore\{x\}=2[x] $
R.H.S. is an integer
$\therefore$ L.H.S. is an integer
$ \therefore\{x\}=0$
$\therefore[x]=0$
$\therefore x=0 $

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