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Q.
Number of solutions of the equation $x^{2}-2-2[x]=0$ ([.] denotes greatest integer function) is
Complex Numbers and Quadratic Equations
Solution:
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.
