Find two numbers whose difference is 108 and whose product is a minimum. (smaller number) (larger number)

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

4x 20 is 80 but if ther machine is broken then there is none you have to redo the test