Java Program to Compute a5+b5 where Value of a and b are Given

Java Program to Compute a5+b5 where Value of a and b are Given

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In the previous article we have discussed Java Program to Compute a4-b4 where Value of a and b are Given

In this program we are going to see how to compute a5+b5   where value of a and b are given by using Java programming language.

Java Program to Compute a5+b5 where Value of a and b are Given

The formula of a5+b5 is given below.

a5+b5  =  (a + b)(a4 – a3b + a2b2 – ab3 + b4)

Now we will convert this into a valid Java expression.

Let x= a5+b5   

=  (a + b)(a4 – a3b + a2b2 – ab3 + b4)

=  a5 – a4b+a3b2 – a2b3 + ab4 + a4b – a3b2 + a2b3 – ab4 + b5

= (a*a*a*a*a) – (a*a*a*a*b) + (a*a*a*b*b) – (a*a*b*b*b) + (a*b*b*b*b)+ (a*a*a*a*b)  – (a*a*a*b*b)  + (a*a*b*b*b)  – (a*b*b*b*b)+ (b*b*b*b*b)

Example:

Suppose a=2 and b=2, then

a5+b5
= (a*a*a*a*a) - (a*a*a*a*b) + (a*a*a*b*b) - (a*a*b*b*b) + (a*b*b*b*b)+ (a*a*a*a*b)  - (a*a*a*b*b)  + (a*a*b*b*b)  - (a*b*b*b*b)+ (b*b*b*b*b)
= (2*2*2*2*2)- (2*2*2*2*2) + (2*2*2*2*2)- (2*2*2*2*2)+ (2*2*2*2*2)+ (2*2*2*2*2)- (2*2*2*2*2)+ (2*2*2*2*2)- (2*2*2*2*2)+ (2*2*2*2*2)
= 64

Now let’s see different ways to compute a5+b5   

Method-1: Java Program to Compute a5+b5 where Value of a and b are Given By Using Static Input Value

Approach:

  • Declare and initialize two integer variables say a and b.
  • By using the formula compute a5+b5  .
  • Print the result.

Program: 

class Main
{
    public static void main(String[] args)
    {
        //declare the first integer variable with an integer value
        int a= 4;
        System.out.println("a= " +a);
        //declare the second integer variable with an integer value
        int b= 2;
        System.out.println("b= "+b);
        //declare another integer variable and assigned the formulated value to it.
        int c= (a*a*a*a*a) - (a*a*a*a*b) + (a*a*a*b*b) - (a*a*b*b*b) + (a*b*b*b*b)+ (a*a*a*a*b)  - (a*a*a*b*b)  + (a*a*b*b*b)  - (a*b*b*b*b)+ (b*b*b*b*b);
        System.out.println("a5 + b5= "+c);
    }
}

Output:

a= 4
b= 2
a5 + b5= 1056

Method-2: Java Program to Compute a5+b5 where Value of a and b are Given By Using User Input Value

Approach:

  • Declare two integer variables say a and b.
  • Take the value of a and b as user input by using Scanner class.
  • Then By using the formula compute a5+b5  .
  • Print the result.

Program:

import java.lang.Math;
import java.util.Scanner;
class Main
{
    public static void main(String[] args)
    {
        //create object of scanner class.
        Scanner sc=new Scanner(System.in);
        System.out.print("a= ");
        //Take the first input from the user.
        int a= sc.nextInt();
        System.out.print("b= ");
        //Take the second input from the user.
        int b= sc.nextInt();
        //declare another integer variable and assigned the formulated value to it.
        double c= (Math.pow(a,5)) - (Math.pow(a,4)*b)+ (Math.pow(a,3)* Math.pow(b,2)) - (Math.pow(a,2)* Math.pow(b,3)) + (a* Math.pow(b,4))+ (Math.pow(a,4)*b)  - (Math.pow(a,3)* Math.pow(b,2))  +(Math.pow(a,2)* Math.pow(b,3))  - (a* Math.pow(b,4))+ (Math.pow(b,5));
        //Typecasting the value of c to integer value
    	System.out.println("a5 + b5= "+(int)c);	
    }
}


Output:

a= 4
b= 5
a5 + b5= 4149

Method-3: Java Program to Compute a5+b5 where Value of a and b are Given By Using User Defined Method

Approach:

  • Declare two integer variables say a and b.
  • Take the value of a and b as user input by using Scanner class.
  • Then call a user defined method say computeValue() and pass a and b as parameter.
  • Then inside method by using the formula compute a5+b5  .
  • Print the result.

Program:

import java.util.Scanner;
class Main
{
    public static void main(String[] args)
    {
        //create object of scanner class.
        Scanner sc=new Scanner(System.in);
        System.out.print("a= ");
        //Take the first input from the user.
        int a= sc.nextInt();
        System.out.print("b= ");
        //Take the second input from the user.
        int b= sc.nextInt();
        //call the function
        computeValue(a,b);
    }
    //define the method
    public static void computeValue(int a, int b)
    {
        //declare another integer variable and assigned the formulated value to it.
        int c= (a*a*a*a*a) - (a*a*a*a*b) + (a*a*a*b*b) - (a*a*b*b*b) + (a*b*b*b*b)+ (a*a*a*a*b)  - (a*a*a*b*b)  + (a*a*b*b*b)  - (a*b*b*b*b)+ (b*b*b*b*b);
        System.out.println("a5 + b5= "+c);
    }
}

Output:

a= 8
b= 10
a5 + b5= 132768

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