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 .
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.