# 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; ` `} ` |

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## 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 ` |

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## 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". ` |

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## 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 ` |

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## 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. ` `?> ` |

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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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