Question

Number of solutions of the equation $x^2-2-2[x]=0$ ([.] denotes greatest integer function) is

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

Answer: (A)

Let us see the graph of $y=x^2-2$ and $y=[x]$

If $[x]=-1$
We have $x^2-2+2=0\Rightarrow x=0$ not possible
$[x]=0\Rightarrow x=\pm \sqrt{2}$ not possible
$[x]=1\Rightarrow x=\pm \sqrt{4}=\pm 2$ not possible
$[x]=2\Rightarrow x=\pm \sqrt{6}$
$\Rightarrow x=\sqrt{6}$ is the only solution.