Question: Let $[t]$ denote the greatest integer $\leq t$. Then the equation in $x,[x]^{2}+2[x+2]-7=0$ has :
no integral solution
exactly four integral solutions
exactly two solutions
infinitely many solutions
Correct Option: , 4
Solution:
$[x]^{2}+2[x+2]-7=0$
$\Rightarrow[x]^{2}+2[x]+4-7=0$
$\Rightarrow[x]=1,-3$
$\Rightarrow x \in[1,2) \cup[-3,-2)$
