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

• Last Updated : 27 Jan, 2023

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 = nÂ·(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 ``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

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## Javascript

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Output

```x is 7
y is 8
z is 56```

Time Complexity: O(1)
Auxiliary Space: O(1)

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

so here x = n, y = 2*n and z = 2*n

Below is the code implementation for the alternate solution

## C++

 `// CPP program to find x y z that satisfies 2/n = 1/x + 1/y + 1/z...``#include ``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 "` `<< 2 * n``             ``<< ``"\nz is "` `<< 2 * n;``}` `// 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` `GFG {``    ``// function to find x, y and z that satisfy given equation.``    ``public` `static` `void` `printXYZ(``int` `n) {``        ``if` `(n == ``1``)``            ``System.out.println(``"-1"``);` `        ``else``            ``System.out.println( ``"x is "` `+ n + ``"\ny is "` `+ ``2` `* n +``                               ``"\nz is "` `+ ``2` `* n);``    ``}` `    ``// driver program to test the above function``    ``public` `static` `void` `main(String[] args) {``        ``int` `n = ``7``;``        ``printXYZ(n);``    ``}``}`

## Javascript

 `// 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)``        ``console.log(-1);` `    ``else``        ``console.log(``"x is "` `+ n + ``"\ny is "` `+ 2 * n``             ``+ ``"\nz is "` `+ 2 * n);``}` `// driver program to test the above function``let n = 7;``printXYZ(n);`

Output

```x is 7
y is 14
z is 14```

Time Complexity: O(1)
Auxiliary Space: O(1)

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