Program to evaluate the expression (√X+1)^6 + (√X-1)^6

Given a number . The task is to find the value of the below expression for the given value of . 

Examples:

Input: X = ?2 
Output: 198 
Explanation: 
= 198
Input: X = 3 
Output: 4160 

Approach: The idea is to use Binomial expression. We can take these two terms as 2 binomial expressions. By expanding these terms we can find the desired sum. Below is the expansion of the terms. 

Now put X= in EQ(1)

Below is the implementation of above approach: 

C++

// CPP program to evaluate the given expression
#include <bits/stdc++.h>
using namespace std;

// Function to find the sum
float calculateSum(float n)
{
    int a = int(n);

    return 2 * (pow(n, 6) + 15 * pow(n, 4)
            + 15 * pow(n, 2) + 1);
}

// Driver Code
int main()
{
    float n = 1.4142;

    cout << ceil(calculateSum(n)) << endl;

    return 0;
}

Java

// Java program to evaluate the given expression
import java.util.*;

class gfg
{
// Function to find the sum
public static double calculateSum(double n)
{
    return 2 * (Math.pow(n, 6) + 15 * Math.pow(n, 4)
            + 15 * Math.pow(n, 2) + 1);
}

// Driver Code
public static void main(String[] args)
{
    double n = 1.4142;
    System.out.println((int)Math.ceil(calculateSum(n)));
}
}
//This code is contributed by mits

Python3

# Python3 program to evaluate
# the given expression

import math

#Function to find the sum
def calculateSum(n):

    a = int(n)

    return (2 * (pow(n, 6) + 15 * pow(n, 4)
            + 15 * pow(n, 2) + 1))

#Driver Code
if __name__=='__main__':
    n = 1.4142
    print(math.ceil(calculateSum(n)))

# this code is contributed by
# Shashank_Sharma

C#

// C# program to evaluate the given expression
using System;
class gfg
{
// Function to find the sum
public static double calculateSum(double n)
{
    return 2 * (Math.Pow(n, 6) + 15 * Math.Pow(n, 4)
            + 15 * Math.Pow(n, 2) + 1);
}

// Driver Code
public static int Main()
{
    double n = 1.4142;
    Console.WriteLine(Math.Ceiling(calculateSum(n)));
    return 0;
}
}
//This code is contributed by Soumik

PHP

<?php
// PHP program to evaluate
// the given expression

//Function to find the sum
function calculateSum($n)
{
    $a = (int)$n;

    return (2 * (pow($n, 6) +
            15 * pow($n, 4) +
            15 * pow($n, 2) + 1));
}

// Driver Code
$n = 1.4142;
echo ceil(calculateSum($n));

// This code is contributed by mits
?>

Javascript

<script>
// javascript program to evaluate the given expression

// Function to find the sum
function calculateSum(n)
{
    return 2 * (Math.pow(n, 6) + 15 * Math.pow(n, 4)
            + 15 * Math.pow(n, 2) + 1);
}

// Driver Code
var n = 1.4142;
document.write(parseInt(Math.ceil(calculateSum(n))));

// This code is contributed by 29AjayKumar
</script>

Output:

198

Time Complexity: O(1)

Auxiliary Space: O(1)