If the ratio of a to b is equal 
to the ratio of b to a, what can you 
say about the two numbers a and b? 
Are they the same or different? 
Justify your answer. 



Cross-multiply and get



Subtract  from both sides: 



Factor 

 

   

So a and b are either the same or else
one is the other with the opposite sign.

The best way to say it is |a| = |b|,
that is, their absolute values
are equal.

1.Solve the following equation by using 
the quadratic formula/completing the square 

           3x² + x + 1 = 0

Using the quadratic formula:

                  ______ 
            -b ± Öb²-4ac
        x = —————————————
                2a 

where a = 3; b = 1; c = 1

                     _____________ 
             -(1) ± Ö(1)²-4(3)(1)
        x = ————————————————————————
                     2(3) 
                   ____ 
             -1 ± Ö1-12
        x = ————————————
                 6

                   ___ 
             -1 ± Ö-11
        x = ———————————
                6

                    __ 
             -1 ± iÖ11
        x = ————————————
                 6 

                      __
             -1     iÖ11
        x = ———— ± —————
              6      6
                      __ 
               1     Ö11
        x = - ——— ± ———— i
               6      6

------------------------------

Completing the square

           

Add -1 to both sides:

               

Multiply every term by 

           

           

Multiply the coeff. of x, which is  by ,
getting .  Then square that, getting ,
then add  to both sides:

           

Factor the left side.  Get LCD on the right

           

Write left side as the square of a binomial, and
combine the terms on the right:

           

Take square roots of both sides:

            = ±

            = ±

            = ±

           ± 
        

2.Solve the following equation by the method 
of your choice:



Cross-multiply:



  

  

  

  

Edwin