The total number of solutions of

x²-4-[x]=0 is(where [.] denotes the greatest integer function).

x²-4-[x]=0

=>x²-4=[x]

Now we plot the graph for y=x²-4 which is an opening upwards parabola with vertex (0,-4)

 Next we plot the graph for y=[x] which is the graph of greayest integer function.

On plotting the graohs we see that the two graphs intersect at two pts.

So the no. of solutions for the given equation are 2.