Okay, being slightly more awake...there's definitely something wrong with your equation...the velocities should subtract instead of add, since if the two particles are moving in the same direction (i.e. have the same sign), then their velocity relative to each other should be less, not more, than if they are moving in opposite directions. Also, the square root term bugs me, since if the particles are moving in opposite directions, (V1)*(V2) will be negative...and the square root will be complex, which doesn't make sense. I'll try deriving an equation for relative velocity using the regular equation later when I have time...