Solve `x^2-4-[x]=0` (where `[]` denotes the greatest integer function).

Explanation

We have `x^(2)-4-[x]=0`
or `x^(2)-4=[x]`
To, solve the equation we first locate the roots, for which we draw the graphs of `y=x^(2)-4 " and " y=[x]` and find the points of intersection.
The graphs of the functions are shown in the following figure.

We observe the graphs intersect when `x^(2) -4=2 " and " x^(2)-4=-2`
`implies x^(2)=6 " or " x^(2)=2`
`implies x=sqrt(6) " or " -sqrt(2)`