Question

The arithmetic mean of two numbers is 18 and the geometric mean is 16. find the sum of squares of the numbers

Answer 1

x+y=36
xy=256

x=256/y
256/y + y = 36

256/y + y²/y = 36y/y

y² - 36y +256 = 0

use the quadratic formula to get 18+2√17 and 18-2√17. ugly numbers but they work!