#include<stdio.h>
#include<conio.h>
#include<math.h>
#define ESP 0.0001
// (x)*(x) + (x)*(y) = 6// (x)*(x) - (y)*(y) = 3#define X(x,y) (x)*(x) + (x)*(y) - 6
#define Y(x,y) (x)*(x) - (y)*(y) - 3
#define F1(x,y) 2*(x) + (y)
#define G1(x,y) 2*(x)
#define F2(x,y) (x)
#define G2(x,y) -(2*(y))


void main()
{
  double x1,y1,y2,x2,x,y,f,g,f1,f2,g1,g2;
  int i=1;
  clrscr();
  printf("\nEnter the value of x: ");
  scanf("%lf",&x);
  printf("\nEnter the value of y: ");
  scanf("%lf",&y);
  f=X(x,y);
  g=Y(x,y);
  printf("\n\nf = %lf",f);
  printf("\n\ng = %lf",g);
  getch();

  f1=F1(x,y);
  f2=F2(x,y);
  g1=G1(x,y);
  g2=G2(x,y);
  printf("\n\nf1 = %lf",f1);
  printf("\n\ng1 = %lf",g1);
  printf("\n\nf2 = %lf",f2);
  printf("\n\ng2 = %lf",g2);
  getch();

  x1= x-((f*g2-g*f2)/(f1*g2-f2*g1));
  y1= y-((g*f1-f*g1)/(f1*g2-f2*g1));
  printf("\n\nx = %lf",x1);
  printf("\n\ny = %lf",y1);
  getch();
  printf("\n\n");
  do
  {
    f=X(x1,y1);
    g=Y(x1,y1);
    printf("\n\nf = %lf",f);
    printf("\n\ng = %lf",g);

    f1=F1(x1,y1);
    f2=F2(x1,y1);
    g1=G1(x1,y1);
    g2=G2(x1,y1);
    printf("\n\nf1 = %lf",f1);
    printf("\n\ng1 = %lf",g1);
    printf("\n\nf2 = %lf",f2);
    printf("\n\ng2 = %lf",g2);

    x2= x1-((f*g2-g*f2)/(f1*g2-f2*g1));
    y2= y1-((g*f1-f*g1)/(f1*g2-f2*g1));
    printf("\n\n x = %lf ",x2);
    printf("\n\n y = %lf ",y2);
    printf("\n\n");

   if(fabs(x1-x2)<ESP && fabs(y1-y2)<ESP)
   {
    printf("\n\nREAL ROOT1 = %.3lf",x1);
    printf("\n\nREAL ROOT2 = %.3lf",y1);
    i=0;
   }
   else
   {
    x1=x2;
    y1=y2;
   }
  }while(i!=0);
getch();
}

/*
____________________________

     OUT PUT
____________________________



Enter the value of x: 1
Enter the value of y: 1

f = -4.000000

g = -3.000000

f1 = 3.000000

g1 = 2.000000

f2 = 1.000000

g2 = -2.000000

 x = 2.375000

 y = 0.875000



f = 1.718750

g = 1.875000

f1 = 5.625000

g1 = 4.750000

f2 = 2.375000

g2 = -1.750000

      x = 2.021820

      y = 0.987796



f = 0.084899

g = 0.112014

f1 = 5.031435

g1 = 4.043639

f2 = 2.021820

g2 = -1.975592

      x = 2.000059

      y = 0.999956



f = 0.000209

g = 0.000326

f1 = 5.000075

g1 = 4.000119

f2 = 2.000059

g2 = -1.999912

      x = 2.000000

      y = 1.000000



REAL ROOT1 = 2.000

REAL ROOT2 = 1.000

 /