Find two positive numbers

Question

Find two positive numbers with product 289 and whose sum is a minimum.

 

Enter your answers in increasing order.

 

First number:

Second Number:

Answer 1

xy = 289 So, y = 289/x

Minimize S = x + y = x + 289x^-1

S' = 1 - 289/x² = (x² - 289) / x²

S' = 0 when x = 17 or -17

By assumption, x is positive. So, minimum when x = 17 and y = 17.