# Nesbitt’s Inequality

Nesbitt’s inequality is one of the simplest inequalities in mathematics. According to the statement of the inequality, for any 3 given real numbers they satisfy the mathematical condition,

for all

Illustrative Examples:

The 3 numbers satisfying Nesbitts inequality are real numbers.

For a = 1, b = 2, c = 3,
the condition of the inequality
{1 / (2 + 3)} + {2 / (1 + 3)} + {3 / (1 + 2)} >= 1.5 holds true.

For a = 1.5, b = 5.6, c = 4.9,
the condition of the inequality
{1.5 / (5.6 + 4.9)} + {5.6 / (1.5 + 4.9)} + {4.9 / (1.5 + 5.6)} >= 1.5 holds true.

For a = 4, b = 6, c = 7,
the condition of the inequality
{4 / (6 + 7)} + {6 / (4 + 7)} + {7 / (4 + 6)} >= 1.5 holds true.

For a = 459, b = 62, c = 783,
the condition of the inequality
{459 / (62 + 783)} + {62 / (459 + 783)} + {783 / (459 + 62)} >= 1.5 holds true.

For a = 9, b = 6, c = 83,
the condition of the inequality
{9 / (6 + 83)} + {6 / (9 + 83)} + {83 / (9 + 6)} >= 1.5 holds true.

## C++

 `// CPP code to verify Nesbitt's Inequality ` `#include ` `using` `namespace` `std; ` ` `  `bool` `isValidNesbitt(``double` `a, ``double` `b, ``double` `c) ` `{ ` `    ``// 3 parts of the inequality sum ` `    ``double` `A = a / (b + c); ` `    ``double` `B = b / (a + c); ` `    ``double` `C = c / (a + b); ` `    ``double` `inequality = A + B + C; ` ` `  `   ``return` `(inequality >= 1.5); ` `} ` ` `  `int` `main() ` `{ ` `    ``double` `a = 1.0, b = 2.0, c = 3.0; ` `    ``if` `(isValidNesbitt(a, b, c))  ` `        ``cout << ``"Nesbitt's inequality satisfied."` `             ``<< ``"for real numbers "` `<< a << ``", "`  `             ``<< b << ``", "` `<< c << ``"\n"``; ` `    ``else` `       ``cout << ``"Not satisfied"``; ` `    ``return` `0; ` `} `

## Java

 `// Java code to verify Nesbitt's Inequality ` `class` `GFG { ` `     `  `    ``static` `boolean` `isValidNesbitt(``double` `a, ` `                          ``double` `b, ``double` `c) ` `    ``{ ` `         `  `        ``// 3 parts of the inequality sum ` `        ``double` `A = a / (b + c); ` `        ``double` `B = b / (a + c); ` `        ``double` `C = c / (a + b); ` `        ``double` `inequality = A + B + C; ` ` `  `        ``return` `(inequality >= ``1.5``); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``double` `a = ``1.0``, b = ``2.0``, c = ``3.0``; ` `        ``if``(isValidNesbitt(a, b, c) == ``true``)  ` `        ``{ ` `            ``System.out.print(``"Nesbitt's inequality"` `                                  ``+ ``" satisfied."``); ` `            ``System.out.println(``"for real numbers "` `                         ``+ a + ``", "` `+ b + ``", "` `+ c); ` `        ``}  ` `        ``else` `            ``System.out.println(``"Nesbitts inequality"` `                                ``+ ``" not satisfied"``); ` `    ``} ` `} ` ` `  `// This code is contributed by JaideepPyne. `

## Python3

 `# Python3 code to verify  ` `# Nesbitt's Inequality ` ` `  `def` `isValidNesbitt(a, b, c): ` `     `  `    ``# 3 parts of the ` `    ``# inequality sum ` `    ``A ``=` `a ``/` `(b ``+` `c); ` `    ``B ``=` `b ``/` `(a ``+` `c); ` `    ``C ``=` `c ``/` `(a ``+` `b); ` `    ``inequality ``=` `A ``+` `B ``+` `C; ` ` `  `    ``return` `(inequality >``=` `1.5``); ` ` `  `# Driver Code ` `a ``=` `1.0``;  ` `b ``=` `2.0``; ` `c ``=` `3.0``; ` `if` `(isValidNesbitt(a, b, c)): ` `    ``print``(``"Nesbitt's inequality satisfied."` `,  ` `          ``" for real numbers "``,a,``", "``,b,``", "``,c); ` `else``: ` `    ``print``(``"Not satisfied"``); ` ` `  `# This code is contributed by mits `

## C#

 `// C# code to verify  ` `// Nesbitt's Inequality ` `using` `System; ` ` `  `class` `GFG ` `{ ` `    ``static` `bool` `isValidNesbitt(``double` `a, ` `                               ``double` `b,  ` `                               ``double` `c) ` `    ``{ ` `         `  `        ``// 3 parts of the ` `        ``// inequality sum ` `        ``double` `A = a / (b + c); ` `        ``double` `B = b / (a + c); ` `        ``double` `C = c / (a + b); ` `        ``double` `inequality = A + B + C; ` ` `  `        ``return` `(inequality >= 1.5); ` `    ``} ` ` `  `    ``// Driver code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `    ``double` `a = 1.0, b = 2.0, c = 3.0; ` `    ``if``(isValidNesbitt(a, b, c) == ``true``)  ` `    ``{ ` `        ``Console.Write(``"Nesbitt's inequality"` `+  ` `                               ``" satisfied "``); ` `        ``Console.WriteLine(``"for real numbers "` `+  ` `                      ``a + ``", "` `+ b + ``", "` `+ c); ` `    ``}  ` `    ``else` `        ``Console.WriteLine(``"Nesbitts inequality"` `+ ` `                               ``" not satisfied"``); ` `    ``} ` `} ` ` `  `// This code is contributed by ajit `

## PHP

 `= 1.5); ` `} ` ` `  `    ``// Driver Code ` `    ``\$a` `= 1.0;  ` `    ``\$b` `= 2.0; ` `    ``\$c` `= 3.0; ` `    ``if` `(isValidNesbitt(``\$a``, ``\$b``, ``\$c``))  ` `        ``echo``"Nesbitt's inequality satisfied."``,  ` `            ``"for real numbers "``, ``\$a``, ``", "``, ``\$b``,  ` `                               ``", "``, ``\$c``, ``"\n"``; ` `    ``else` `    ``cout <<``"Not satisfied"``; ` ` `  ` `  `// This code is contributed by Ajit. ` `?> `

Output :

```Nesbitt's inequality satisfied.for real numbers 1, 2, 3
```

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