SOLUTION: The product of two consecutive odd integers is 63.Find the numbers. 1.What information is given? 2.what are you asked to find? 3.Write a representation using variable x. 4.Wh

1)  First, you may simply GUESS the answer:  63 = 7*9.

    When you guessed it, your next thought is that two opposite numbers give the same product

    and also represent two consecutive odd integers -9,-7.


    So, by guessing, you have these two answers (two pairs)  (7,9)  and  (-9,-7).




2)  You may also take the square root of 63:    is somewhere close to   = 8.


    Therefore, your next thought is about the numbers 7 and 9,

    and then you continue as in n.1).




3)  You may denote the smaller of the two consecutive odd numbers as x;  then the next odd integer number is (x+2).


    In this way, you get this equation

       x*(x+2) = 63.


    You reduce it then to the standard algebraic form

       x^2 + 2x - 63 = 0.


    You may solve it by factoring 

       (x+9)*(x-7) = 0

    which gives you the roots  x= -9,  x= 7.


    The first root gives the solution (the pair) (-9,-7);  the other root gives you the pair (7,9).


    We just observed these pairs in the above version 1) and 2).


    You also may solve equation (1) using the quadratic formula.