Use display, or display3d--- it doesn't matter which. No capital D though. I needed to put a colon at the end of your first line and correct the spelling of "implicit" in your last line.
If you're happy with the plot, save it to a variable:
Again, save it to a variable:
All that being said, an implicit plot is not a great choice for this problem, seeing as how your equations are already solved for z. You could just do this:
plot3d([x^2+y^2, 2-x^2-y^2], x= -5..5, y= -5..5);