Mathomatic version 14.1.6 (www.mathomatic.org)
Copyright (C) 1987-2008 George Gesslein II.
100 equation spaces available, 960K per equation space.
HTML bold color mode enabled.
1—> ; Combine 3 quadratic polynomial equations with 3 unknown coefficients (a, b, c).
1—> ; Solve for variables (a), (b), and (c).
1—> 
1—> clear all ; restart Mathomatic
1—> ; enter all 3 equations:
1—> y1=a+b*x1+c*x1^2

#1: y1 = a + (b·x1) + (c·(x1^2))

1—> y2=a+b*x2+c*x2^2

#2: y2 = a + (b·x2) + (c·(x2^2))

2—> y3=a+b*x3+c*x3^2

#3: y3 = a + (b·x3) + (c·(x3^2))

3—> 2 ; select equation number 2

#2: y2 = a + (b·x2) + (c·(x2^2))

2—> eliminate a ; eliminate variable (a) from the current equation
Solving equation #1 for (a) and substituting into the current equation...

#2: y2 = (b·x2) − (x1·(b + (c·x1))) + y1 + (c·(x2^2))

2—> 3 ; select equation number 3

#3: y3 = a + (b·x3) + (c·(x3^2))

3—> eliminate a b ; eliminate variables (a) and (b)
Solving equation #1 for (a) and substituting into the current equation...
Solving equation #2 for (b) and substituting into the current equation...

         (y1 − y2 + (c·((x2^2) − (x1^2))))·x3        (y1 − y2 + (c·((x2^2) − (x1^2))))
#3: y3 = ———————————————————————————————————— − (x1·(————————————————————————————————— + (c·x1))) + y1 + (c·(x3^2))
                      (x1 − x2)                                  (x1 − x2)

3—> c ; find (c)

               ((y2·(x1 − x3)) + (y1·(x3 − x2)) − (y3·(x1 − x2)))
#3: c = —————————————————————————————————————————————————————————————————
        ((x1·((x2^2) + (x1·(x3 − x2)))) − (x3·((x2^2) + (x3·(x1 − x2)))))

3—> simplify

         (y1 − y2)   (y3 − y2)
        (————————— + —————————)
         (x2 − x1)   (x3 − x2)
#3: c = ———————————————————————
               (x3 − x1)

3—> 2 ; select equation number 2 again

        (y1 − y2 + (c·((x2^2) − (x1^2))))
#2: b = —————————————————————————————————
                    (x1 − x2)

2—> eliminate c using 3 ; find (b)
Solving equation #3 for (c) and substituting into the current equation...

                   (((y1 − y2)·(x3 − x2)) + ((y3 − y2)·(x2 − x1)))·((x2^2) − (x1^2))
        (y1 − y2 + —————————————————————————————————————————————————————————————————)
                                    ((x2 − x1)·(x3 − x2)·(x3 − x1))
#2: b = —————————————————————————————————————————————————————————————————————————————
                                          (x1 − x2)

2—> simplify
Division simplified with polynomial GCD.

        (((x1^2)·(y3 − y2)) + ((x2^2)·(y1 − y3)) + ((x3^2)·(y2 − y1)))
#2: b = ——————————————————————————————————————————————————————————————
                       ((x2 − x1)·(x3 − x1)·(x3 − x2))

2—> 1 ; select equation number 1

#1: a = -1·((x1·(b + (c·x1))) − y1)

1—> eliminate b c ; find (a)
Solving equation #2 for (b) and substituting into the current equation...
Solving equation #3 for (c) and substituting into the current equation...

                 (((x1^2)·(y3 − y2)) + ((x2^2)·(y1 − y3)) + ((x3^2)·(y2 − y1)))   (((y1 − y2)·(x3 − x2)) + ((y3 − y2)·(x2 − x1)))·x1
#1: a = -1·((x1·(—————————————————————————————————————————————————————————————— + ——————————————————————————————————————————————————)) − y1)
                                ((x2 − x1)·(x3 − x1)·(x3 − x2))                            ((x2 − x1)·(x3 − x2)·(x3 − x1))

1—> simplify

                      ((x3·(((x1^2)·y2) − (y1·(x2^2)))) + ((x3^2)·((y1·x2) − (x1·y2))))
        ((x1·x2·y3) + —————————————————————————————————————————————————————————————————)
                                                  (x2 − x1)
#1: a = ————————————————————————————————————————————————————————————————————————————————
                                     ((x1 − x3)·(x2 − x3))

1—> fraction all ; list all solutions, converting to simple fractions

        ((x1·x2·y3·(x2 − x1)) + (x3·(((x1^2)·y2) − (y1·(x2^2)) + (x3·((y1·x2) − (x1·y2))))))
#1: a = ————————————————————————————————————————————————————————————————————————————————————
                                  ((x2 − x1)·(x1 − x3)·(x2 − x3))


        (((x1^2)·(y3 − y2)) + ((x2^2)·(y1 − y3)) + ((x3^2)·(y2 − y1)))
#2: b = ——————————————————————————————————————————————————————————————
                       ((x2 − x1)·(x3 − x1)·(x3 − x2))


        (((y1 − y2)·(x3 − x2)) + ((y3 − y2)·(x2 − x1)))
#3: c = ———————————————————————————————————————————————
                ((x2 − x1)·(x3 − x2)·(x3 − x1))

Finished reading file "poly.in".
1—> 
End of input.