Because both (root number a+b-2006) and (root number 2006-a-b) should be greater than or equal to 0.

And (radical number a+b-2006)× (radical number 2006-a-b)= the square of radical number -(2006-a-b).

Because the square of (2006-a-b) must be greater than or equal to zero, the square of the root number -(2006-a-b) should be consistent with the meaning of the question, and the square of the root number -(2006-a-b) should be 0.

According to the characteristics of the equation, we can get: (root number 3y-8)=0, (root number 5x-3)=0.

So 3y=8 and 5x=3.

So 5X+3Y= 1 1.