This one is a little different than the other illuminations problems I have seen.

Well, let's have a go.

Let S be the illumination at a point P which is, say, x units from the first source.

Let the two sources be .

when

Can you finish solving for x?. Remember that

or . Whatever. The problem does not specify.

That way you can eliminate a variable.

You can use the 2nd derivative test to check the point to see if it is the minimum, but it most likely will be.