Let x---------------> smaller number y----------------> larger number
we know that y-x=108---------> y=108+x
product------------> x*y-------> x*(108+x)-----> 108x+x² find the derivative and equals to zero dx/dy=108+2x-------------> 108+2x=0---------> 2x=-108--------> x=-54 then y=108+x-------> y=108-54-----> y=54
the answer is smaller number is -54 larger number is 54
