Find two positive numbers whose product is 25 and whose sum is a minimum. (if both values are the same number, enter it into both blanks.) (smaller number) (larger number)

Let the numbers be x and y:

xy=25

⇒y=25/x

the sum of the numbers is:

S=x+y

S=x+25/x

S=x+25x^-1

For minimum perimeter

S' (x) = 0

thus

S' (x) = 1-25x^-2=0

solving for x:

1-25x^-2=0

1=25/x^2

hence

x^2=25

thus

x=5

for manimum sum the numbers should be x=5 and y=5