Find Harmonic mean using Arithmetic mean and Geometric mean

Given two numbers, first calculate arithmetic mean and geometric mean of these two numbers. Using the arithmetic mean and geometric mean so calculated, find the harmonic mean between the two numbers.

Examples: 

Input : a = 2
 b = 4
Output : 2.666

Input : a = 5
 b = 15
Output : 7.500

Arithmetic Mean: Arithmetic Mean 'AM' between two numbers a and b is such a number that AM-a = b-AM. Thus, if we are given these two numbers, the arithmetic mean AM = 1/2(a+b)
Geometric Mean: Geometric Mean 'GM' between two numbers a and b is such a number that GM/a = b/GM. Thus, if we are given these two numbers, the geometric mean GM = sqrt(a*b)
Harmonic Mean: Harmonic Mean 'HM' between two numbers a and b is such a number that 1/HM - 1/a = 1/b - 1/HM. Thus, if we are given these two numbers, the harmonic mean HM = 2ab/a+b
Now, we also know that 

Output: 

Harmonic Mean between 5 and 15 is 7.500

Time Complexity: O(log(a*b)), for using sqrt function where a and b represents the given integers. 
Auxiliary Space: O(1), no extra space is required, so it is a constant.