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# 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

## C++

 // C++ implementation of computation  of// arithmetic mean, geometric mean// and harmonic mean#include using namespace std;  // Function to calculate arithmetic // mean, geometric mean and harmonic meandouble compute(int a, int b){      double AM, GM, HM;      AM = (a + b) / 2;    GM = sqrt(a * b);    HM = (GM * GM) / AM;    return HM;}  // Driver functionint main(){      int a = 5, b = 15;    double HM = compute(a, b);    cout << "Harmonic Mean between " << a           << " and " << b << " is " << HM ;    return 0;}

## Java

 // Java implementation of computation  of// arithmetic mean, geometric mean// and harmonic meanimport java.io.*;  class GeeksforGeeks {          // Function to calculate arithmetic     // mean, geometric mean and harmonic mean    static double compute(int a, int b)    {          double AM, GM, HM;          AM = (a + b) / 2;        GM = Math.sqrt(a * b);        HM = (GM * GM) / AM;        return HM;    }          // Driver function    public static void main(String args[])    {        int a = 5, b = 15;        double HM = compute(a, b);        String str = "";        str = str + HM;        System.out.print("Harmonic Mean between "                           + a + " and " + b + " is "                           + str.substring(0, 5));    }}

## Python3

 # Python 3 implementation of computation # of arithmetic mean, geometric mean# and harmonic mean  import math   # Function to calculate arithmetic # mean, geometric mean and harmonic meandef compute( a, b) :    AM = (a + b) / 2    GM = math.sqrt(a * b)    HM = (GM * GM) / AM    return HM  # Driver functiona = 5b = 15HM = compute(a, b)print("Harmonic Mean between " , a,      " and ", b , " is " , HM )    # This code is contributed by Nikita Tiwari.

## C#

 // C# implementation of computation  of// arithmetic mean, geometric mean// and harmonic meanusing System;  class GeeksforGeeks {          // Function to calculate arithmetic     // mean, geometric mean and harmonic mean    static double compute(int a, int b)    {          double AM, GM, HM;          AM = (a + b) / 2;        GM = Math.Sqrt(a * b);        HM = (GM * GM) / AM;        return HM;    }          // Driver function    public static void Main()    {        int a = 5, b = 15;        double HM = compute(a, b);        Console.WriteLine("Harmonic Mean between "                        + a + " and " + b + " is "                        +HM);    }}// This code is contributed by mits



## Javascript



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.