Java Program to Compute a4+a2+1 where Value of a is Given

In the previous article we have discussed Java Program to Compute a4+a2b2+b4 where Value of a and b are Given

In this program we are going to see how to compute a⁴+a²+1 where value of a is given by using Java programming language.

Java Program to Compute a4+a2+1 where Value of a is Given

The formula of a⁴+a²+1 is given below.

a⁴+a²+1 = (a² – a + 1)(a² + a + 1)

Now we will convert this into a valid Java expression.

Let x= a⁴+a²+1

= (a2 – a + 1)(a2 + a + 1)

= ((a*a) – a + 1)*( (a*a) + a + 1)

Example:

Suppose a=2 and b=2, Then

a4+a2+1 
= ((a*a) - a + 1)*( (a*a) + a + 1)
= ((2*2) - 2 + 1)*( (2*2) + 2 + 1)
= 21

Now let’s see different ways to compute a⁴+a²+1

By Using Static Input Value
By Using User Input Value and Pow() Function
By Using User Defined Method

Method-1: Java Program to Compute a4+a2+1 where Value of a is Given By Using Static Input Value

Approach:

Declare and initialize an integer variables say a.
By using the formula compute a⁴+a²+1
Print the result.

Program:

class Main
{
    public static void main(String[] args)
    {
        //declare the first integer variable with a integer value
        int a= 4;
        System.out.println("a= " +a);
        //declare another integer variable and assigned the formulated value to it.
        int c= ((a*a) - a + 1)*( (a*a) + a + 1);
        System.out.println("a4+a2+1= "+c);
    }
}

Output:

a= 4
a4+a2+1= 273

Method-2: Java Program to Compute a4+a2+1 where Value of a is Given By Using User Input Value and Pow() Function

Approach:

Declare an integer variables say a.
Prompt the user to enter the values to the corresponding variables by using Scanner class.
Then By using the formula compute a⁴+a²+1
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();
        //declare another integer variable and assigned the formulated value to it.
        double c=( Math.pow(a,2)-a+1)*( Math.pow(a,2)+a+1);
        //Typecasting the value of c to integer value
        System.out.println("a4+a2+1= "+(int)c);	
    }
}

Output:

a= 20
a4+a2+1= 160401

Method-3: Java Program to Compute a4+a2+1 where Value of a is Given By Using User Defined Method

Approach:

Declare an integer variables say a .
Prompt the user to enter the values to the corresponding variables by using Scanner class.
Then call a user defined method say computeValue() and pass a as parameter.
Then inside method by using the formula compute a⁴+a²+1
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();
        //call the function
        computeValue(a);
    }
    
    //define the method
    public static void computeValue(int a)
    {
        //declare another integer variable and assigned the formulated value to it.
        int c= ((a*a) - a + 1)*( (a*a) + a + 1);
        System.out.println("a4+a2+1= "+c);
    }
}

Output:

a= 10
a4+a2+1= 10101

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