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Nesbitt’s Inequality
• Last Updated : 05 May, 2021

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++

 `// C++ 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.``?>`

## Javascript

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

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