Question:
Let $[t]$ denote the greatest integer $\leq t$. Then the equation in $x,[x]^{2}+2[x+2]-7=0$ has:
Correct Option: , 4
Solution:
The given equation
$[x]^{2}+2[x]+4-7=0$
$\Rightarrow[x]^{2}+2[x]-3=0$
$\Rightarrow[x]^{2}+3[x]-[x]-3=0$
$\Rightarrow([x]+3)([x]-1)=0 \Rightarrow[x]=1$ or $-3$
$\Rightarrow x \in[-3,-2) \cup[1,2)$
$\therefore$ The equation has infinitely many solutions.
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