find the two numbers whose sum of the squares is a minimum if the product of the numbers is 10.

Answer 1

xy = 10, so y=10/x

z = x^2+y^2 = x^2 + 100/x^2
dz/dx = 2x - 200/x^3
= (2x^2-200)/x^3

dz/dx=0 when x=±10

Answer 2

find two numbers whose product is 16 and whose sum of squares is minimum.