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
