MCQ
The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has:
- Aexactly two solutions in $(-\infty, \infty)$
- Bno solution
- Ca unique solution in $(-\infty, 1)$
- ✓a unique solution in $(-\infty, \infty)$
$\Rightarrow x^2-4 x+3=x[x]-[x]$
$\Rightarrow(x-1)(x-3)=[x] .(x-1)$
$\Rightarrow x=1 \text { or } x-3=[x]$
$\Rightarrow x-[x]=3$
$\Rightarrow\{x\}=3 \text { (Not Possible) }$
Only one solution $x=1$ in $(-\infty, \infty)$
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