Find the greatest product using rational rational numbers with a sum of 20

Hello,

Let's be x and y the 2 numbers

x+y=20==>y=20-x

P (x) = x*y=x * (20-x) = 20x-x²

Max (P (x)) = = >P' (x) = 0 = 20-2x==>2x=20==>x=10

A product is maximum is the 2 numbers are equals;

Numbers are 10 and 10 and product=100