Question

The arithmetic and geometric mean of two numbers are 17 and 15 respectively.find out the numbers.

Answer 1

Let the numbers be a and b.

their arithmetic mean,

(a+b)/2 = 17 => a+b = 34

their geometric mean,

√ab = 15 => ab = 225

(a - b)² = (a + b) ² - 4ab = 34² - 4(225) = 1156 - 900 = 256

=> a - b = 16

solving a+b = 34 and a - b = 16

we get, a = 25, b = 9