Skip to content
Related Articles

Related Articles

Improve Article

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

  • Last Updated : 22 Mar, 2021

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

(\sqrt[]{X} +1)^6 + (\sqrt[]{X}-1)^6

Examples: 
 

Input: X = √2 
Output: 198 
Explanation2[(\sqrt[]{2})^6 + 15 (\sqrt[]{2})^4 + 15\sqrt[]{2})^2 + 1]
= 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. 
 



\newline (X+1)^6 = {6_C}_0 X^6+6_c_1 X^5+{6_C}_2 X^4+{6_C}_3 X^3+{6_C}_4 X^2+{6_C}_5 X+{6_C}_6 \newline (X-1)^6 = {6_C}_0 X^6-6_c_1 X^5+{6_C}_2 X^4-{6_C}_3 X^3+{6_C}_4 X^2-{6_C}_5 X+{6_C}_6 \newline (X+1)^6+(X-1)^6 =2[{6_C}_0 X^6+{6_C}_2 X^4+{6_C}_4 X^2+{6_C}_6] \newline \newline (X+1)^6+(X-1)^6=2[X^6 + 15 X^4 + 15 X^2 +1] ---EQ(1)
 

Now put X=   in EQ(1)
 

\newline (\sqrt[]{2}+1)^6+(\sqrt[]{2}-1)^6 = 2[(\sqrt[]{2})^6 + 15 (\sqrt[]{2})^4 + 15\sqrt[]{2})^2 + 1] \newline = 2(8 + 15 x 4 + 15 x 2 + 1 ) \newline = 2(8 + 60 + 30 + 1) \newline = 198
 

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

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.




My Personal Notes arrow_drop_up
Recommended Articles
Page :