#include <iostream>
#include <cmath>
#include <iomanip>
 
using namespace std;
 
// ফাংশন সংজ্ঞা: f(x) = x^3 - x - 3
double f(double x) {
    return pow(x, 3) - x - 3;
}
 
int main() {
    double x1, x2, x3, f1, f2;
    const double tolerance = 1e-6;
    const int max_iterations = 100;
    int iteration = 1;
 
    // প্রাথমিক অনুমান গ্রহণ
    cout << "Enter the value of x1: ";
    cin >> x1;
    cout << "Enter the value of x2: ";
    cin >> x2;
 
    cout << fixed << setprecision(6);
    cout << "\nIteration\tx1\t\tx2\t\tx3\t\tf(x1)\t\tf(x2)\n";
 
    while (iteration <= max_iterations) {
        f1 = f(x1);
        f2 = f(x2);
 
        // বিভাজক খুব ছোট হলে লুপ থেকে বেরিয়ে আসা
        if (fabs(f2 - f1) < 1e-12) {
            cout << "Denominator too small. Division by zero risk.\n";
            break;
        }
 
        // নতুন আনুমানিক মান নির্ণয়
        x3 = (f2 * x1 - f1 * x2) / (f2 - f1);
 
        // বর্তমান ইটারেশনের মান প্রদর্শন
        cout << iteration << "\t\t" << x1 << "\t" << x2 << "\t" << x3 << "\t" << f1 << "\t" << f2 << "\n";
 
        // কনভার্জেন্স পরীক্ষা
        if (fabs((x3 - x2) / x3) < tolerance) {
            cout << "\nApproximate root = " << x3 << endl;
            break;
        }
 
        // পরবর্তী ইটারেশনের জন্য মান আপডেট
        x1 = x2;
        x2 = x3;
        iteration++;
    }
 
    if (iteration > max_iterations) {
        cout << "Method did not converge within the maximum number of iterations.\n";
    }
 
    return 0;
}
 

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Enter the value of x1: 4
Enter the value of x2: 2