Gradient and blending of colours

["Richard" <lb_email@xxxxxxxxxxxx>]

Just downloaded GIMP. Absolute beginner.

Lets say that your image boundary is triangular in shape.

The task is to have the three primary colours seemingly emanate from 
spots located near each corner of a triangle. The colours should fade 
at the rate that light diminishes with distance, so the colours need to 
go through a gradient.

The requirement is also that the colours merge or blend together in the 
image. If you can do that, then the centre of the triangle would of 
course be white.

Can you with GIMP get an effect like having three lamps (Red Green 
Blue) spaced in a triangle on a white wall? That's basically what I'm 
trying to do.

Can anyone advise how I might create the image I'm seeking to produce? 
TIA.