MNUM

#include <iostream>
#include <math.h>
#include <iomanip>

using namespace std;

double f(double x) {
	return x - 2 * log(x) - 5;
}

double f1(double x) {
	return sqrt(2 * x + 5);
}

double f2(double x) {
	return x*x - 20;
}

bool bissecao(double a, double b){

	double xn;
	int i=1;

	while (i <= 100) {
		xn = (a + b) / 2;

		if (f(a)*f(xn) > 0) {
			a = xn;
		}
		else b = xn;



		cout << i << " / " << fixed << setw(8) << a << " / " << xn << " / " << b << " / " <<  f(a) << " / " << f(xn) << " / " << f(b) << endl;

			i++;
	}



	return true;
}

bool bissecao(double a, double b, double e) {

	double xn = (a+b)/2, xna;
	int i = 0;

	do {
		xna = xn;

		cout << i << " / " << fixed << setw(5) << a << " / " << xn << " / " << b << " / " << f(a) << " / " << f(xn) << " / " << f(b) << endl;


		if (f(a)*f(xn) > 0) {
			a = xn;
		}
		else b = xn;






		xn = (a + b) / 2;

		i++;
	} while (abs(xn - xna) > e);



	return true;
}

bool corda(double a, double b, double e) {


	double xn = (a*f(b)-b*f(a))/(f(b)-f(a)), xna;
	int i = 0;

	do {
		xna = xn;

		cout << i << " / " << fixed << setw(5) << a << " / " << xn << " / " << b << " / " << f(a) << " / " << f(xn) << " / " << f(b) << endl;


		if (f(a)*f(xn) > 0) {
			a = xn;
		}
		else b = xn;






		xn = (a*f(b) - b*f(a)) / (f(b) - f(a));

		i++;
	} while (abs(xn - xna) > e);





	return true;
}

bool newton(double a, double b, double e, double xn) {

	double xna = 999999999;
	int i=0;

	while (abs(xn - xna) > e) {

		cout << i << " / " << fixed << setw(5) << a << " / " << xn << " / " << b << " / " << f(a) << " / " << f(xn) << " / " << f(b) << endl;

		xna = xn;

		xn = xna - f(xna) / (1 - (2 / xna));




		i++;

	}

	return true;

}

bool picardpeano1() {

	/*y^2 - 2x -5 = 0
	  x^2 -y - 20 = 0*/



	double x0, y0, x, y;
	int i;

	cout << "Guess: (x, y)\n";
	cin >> x0 >> y0;

	for (i = 0; i <= 50; i++) {
		cout << i << " / "  << x0 << " / " << y0 << endl;

		x = (y0*y0 - 5) / 2.0;
		y = x0*x0 - 20.0;
		x0 = x;
		y0 = y;



	}



	return true;
}

bool picardpeano2() {

	/*y^2 - 2x -5 = 0
	x^2 -y - 20 = 0*/



	double x0, y0, x, y;
	int i;

	cout << "Guess: (x, y)\n";
	cin >> x0 >> y0;

	for (i = 0; i <= 50; i++) {
		cout << i << " / " << x0 << " / " << y0 << endl;

		x = sqrt(y0 + 20);
		y = sqrt(2 * x0 + 5);
		x0 = x;
		y0 = y;



	}

	//NÂO ESQUECER DO RESIDUO

	cout << y0*y0 - 2*x0 - 5;



	return true;
}

int main() {

	double a = 9, b = 10, e=0.0001, guess = 0.1;

	picardpeano2();



	return 0;
}