Suppose the product of 𝑥 x and 𝑦 y is 25 and both 𝑥 x and 𝑦 y are positive. What is the minimum possible sum of 𝑥 x and 𝑦 y ? The minimal possible sum is

Question

Suppose the product of  and  is 25 and both  and  are positive. What is the minimum possible sum of  and ? The minimal possible sum is 

Answer 1

XY=25

X+y = x+25/x = f(x)

x+ 25*x^(-1) = f(x)

1 - 25 x^(-2) = f'(x)

minimum occurs at 0 = f'(x)

0 = 1 - 25 x^(-2)

0 = x^2 - 25

x = 5 or x = -5

since they are positive, x=5 --> y = 5