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,
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++ code to verify Nesbitt's Inequality #include <bits/stdc++.h> 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 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 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# 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 // PHP code to verify // Nesbitt's Inequality function 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 ))
echo "Nesbitt's inequality satisfied." ,
"for real numbers " , $a , ", " , $b ,
", " , $c , "\n" ;
else
cout << "Not satisfied" ;
// This code is contributed by Ajit. ?> |
<script> // Javascript code to verify Nesbitt's Inequality function isValidNesbitt(a, b, c)
{ // 3 parts of the
// inequality sum
let A = a / (b + c);
let B = b / (a + c);
let C = c / (a + b);
let inequality = A + B + C;
return (inequality >= 1.5);
} // Driver code let a = 1.0, b = 2.0, c = 3.0; if (isValidNesbitt(a, b, c) == true )
{ document.write( "Nesbitt's inequality" +
" satisfied." );
document.write( "for real numbers " +
a + ", " + b + ", " + c);
} else document.write( "Nesbitts inequality" +
" not satisfied" );
// This code is contributed by decode2207 </script> |
Output :
Nesbitt's inequality satisfied.for real numbers 1, 2, 3
Time complexity : O(1)
Auxiliary Space : O(1)