Question

Let [t] denote the greatest integer $\le t$. Then the equation in $x,[x{]}^2+2[x+2]-7=0$ has:

• A. no integral solution
• B. exactly four integral solutions
• C. exactly two solutions
• D. infinitely many solutions

Answer 1

Answer: (D)

$[x{]}^2+2[x+2]-7=0$
$\Rightarrow [x{]}^2+2[x]+4-7=0$
$\Rightarrow [x]=1,-3$
$\Rightarrow x\in [1,2)\cup [-3,-2)$