Nesbitt不等式是数学中最简单的不等式之一。根据不等式的陈述,对于任何3个给定的实数,它们都满足数学条件,
对所有人
说明性示例:
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.
?>
Nesbitt's inequality satisfied.for real numbers 1, 2, 3