Question

If the ratio of harmonic mean of two numbers to their geometric mean is 12 : 13, find the ratio of the numbers.

Answer 1

Let a and b be two numbers.

Harmonic Mean, HM = 2ab(a+b)

geometric Mean, GM = √(ab)

2ab(a+b) : √(ab) = 12:13

(a+b)/√(ab) = 13/6

√(a/b) +√(b/a) = 13/6

Let √(a/b) = x

x + 1/x = 13/6

6x2 - 13x + 6 = 0

x = 2/3 or 3/2

a/b = x2

a/b = 4/9 

Answer 2

Answer:

Step-by-step explanation: