# Find x, y, z that satisfy 2/n = 1/x + 1/y + 1/z

Given n, find x, y, z such that x, y, z satisfy the equation “2/n = 1/x + 1/y + 1/z”

There are multiple x, y and z that satisfy the equation print anyone of them, if not possible then print -1.

Examples:

Input : 3 Output : 3 4 12 Explanation: here 3 4 and 12 satisfy the given equation Input : 7 Output : 7 8 56

Note that for n = 1 there is no solution, and for n > 1 there is solution x = n, y = n+1, z = n·(n+1).

To come to this solution, represent 2/n as 1/n+1/n and reduce the problem to represent 1/n as a sum of two fractions. Let’s find the difference between 1/n and 1/(n+1) and get a fraction 1/(n*(n+1)), so the solution is

2/n = 1/n + 1/(n+1) + 1/(n*(n+1))

## C++

`// CPP program to find x y z that` `// satisfies 2/n = 1/x + 1/y + 1/z...` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// function to find x y and z that` `// satisfy given equation.` `void` `printXYZ(` `int` `n)` `{` ` ` `if` `(n == 1)` ` ` `cout << -1;` ` ` `else` ` ` `cout << ` `"x is "` `<< n << ` `"\ny is "` ` ` `<< n + 1 << ` `"\nz is "` ` ` `<< n * (n + 1);` `}` `// driver program to test the above function` `int` `main()` `{` ` ` `int` `n = 7;` ` ` `printXYZ(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find x y z that` `// satisfies 2/n = 1/x + 1/y + 1/z...` `import` `java.io.*;` `class` `Sums {` ` ` `// function to find x y and z that` ` ` `// satisfy given equation.` ` ` `static` `void` `printXYZ(` `int` `n){` ` ` `if` `(n == ` `1` `)` ` ` `System.out.println(-` `1` `);` ` ` `else` `{` ` ` `System.out.println(` `"x is "` `+ n);` ` ` `System.out.println(` `"y is "` `+ (n+` `1` `));` ` ` `System.out.println(` `"z is "` `+ (n * (n + ` `1` `)));` ` ` `}` ` ` `}` ` ` `// Driver program to test the above function` ` ` `public` `static` `void` `main (String[] args) {` ` ` `int` `n = ` `7` `;` ` ` `printXYZ(n);` ` ` `}` `}` `// This code is contributed by Chinmoy Lenka` |

## Python3

`# Python3 code to find x y z that` `# satisfies 2/n = 1/x + 1/y + 1/z...` `# function to find x y and z that` `# satisfy given equation.` `def` `printXYZ( n ):` ` ` `if` `n ` `=` `=` `1` `:` ` ` `print` `(` `-` `1` `)` ` ` `else` `:` ` ` `print` `(` `"x is "` `, n )` ` ` `print` `(` `"y is "` `,n ` `+` `1` `)` ` ` `print` `(` `"z is "` `,n ` `*` `(n ` `+` `1` `))` `# driver code to test the above function` `n ` `=` `7` `printXYZ(n)` `# This code is contributed by "Sharad_Bhardwaj".` |

## C#

`// C# program to find x y z that` `// satisfies 2/n = 1/x + 1/y + 1/z...` `using` `System;` `class` `GFG` `{` ` ` `// function to find x y and z that` ` ` `// satisfy given equation.` ` ` `static` `void` `printXYZ(` `int` `n)` ` ` `{` ` ` `if` `(n == 1)` ` ` `Console.WriteLine(-1);` ` ` `else` ` ` `{` ` ` `Console.WriteLine(` `"x is "` `+ n);` ` ` `Console.WriteLine(` `"y is "` `+ (n+1));` ` ` `Console.WriteLine(` `"z is "` `+ (n * (n + 1)));` ` ` `}` ` ` `}` ` ` ` ` `// Driver program` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` `int` `n = 7;` ` ` `printXYZ(n);` ` ` `}` `}` `// This code is contributed by vt_m` |

## PHP

`<?php` `// PHP program to find x y z that` `// satisfies 2/n = 1/x + 1/y + 1/z...` `// function to find x y and z that` `// satisfy given equation.` `function` `printXYZ(` `$n` `)` `{` ` ` `if` `(` `$n` `== 1)` ` ` `echo` `-1;` ` ` `else` ` ` `echo` `"x is "` `, ` `$n` `, ` `"\ny is "` ` ` `, ` `$n` `+ 1 , ` `"\nz is "` `,` ` ` `$n` `* (` `$n` `+ 1);` `}` ` ` `// Driver Code` ` ` `$n` `= 7;` ` ` `printXYZ(` `$n` `);` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// Javascript program to find x y z that` `// satisfies 2/n = 1/x + 1/y + 1/z...` `// function to find x y and z that` `// satisfy given equation.` `function` `printXYZ(n)` `{` ` ` `if` `(n == 1)` ` ` `document.write(-1);` ` ` `else` ` ` `document.write(` `"x is "` `+ n + ` `"<br>y is "` ` ` `+ (n + 1) + ` `"<br>z is "` ` ` `+ n * (n + 1));` `}` `// driver program to test the above function` ` ` `let n = 7;` ` ` `printXYZ(n);` `</script>` |

**Output: **

x is 7 y is 8 z is 56

**Time complexity:** O(1)**Alternate Solution**

We can write 2/n = 1/n + 1/n. And further as 2/n = 1/n + 1/2n + 1/2n.

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