# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 compution of ` `// arithmetic mean, geometric mean ` `// and harmonic mean ` `#include ` `using` `namespace` `std; ` ` `  `// Function to calculate arithmetic  ` `// mean, geometric mean and harmonic mean ` `double` `compute(``int` `a, ``int` `b) ` `{ ` ` `  `    ``double` `AM, GM, HM; ` ` `  `    ``AM = (a + b) / 2; ` `    ``GM = ``sqrt``(a * b); ` `    ``HM = (GM * GM) / AM; ` `    ``return` `HM; ` `} ` ` `  `// Driver function ` `int` `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 compution of ` `// arithmetic mean, geometric mean ` `// and harmonic mean ` `import` `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 compution ` `# of arithmetic mean, geometric mean ` `# and harmonic mean ` ` `  `import` `math  ` ` `  `# Function to calculate arithmetic  ` `# mean, geometric mean and harmonic mean ` `def` `compute( a, b) : ` `    ``AM ``=` `(a ``+` `b) ``/` `2` `    ``GM ``=` `math.sqrt(a ``*` `b) ` `    ``HM ``=` `(GM ``*` `GM) ``/` `AM ` `    ``return` `HM ` ` `  `# Driver function ` `a ``=` `5` `b ``=` `15` `HM ``=` `compute(a, b) ` `print``(``"Harmonic Mean between "` `, a, ` `      ``" and "``, b , ``" is "` `, HM ) ` ` `  ` `  `# This code is contributed by Nikita Tiwari. `

## C#

 `// C# implementation of compution of ` `// arithmetic mean, geometric mean ` `// and harmonic mean ` `using` `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 `

## PHP

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Output:

```Harmonic Mean between 5 and 15 is 7.500
```

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