Q&A #9409

Teachers' Lounge Discussion: Solving algebraic equations

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From: John

To: Teacher2Teacher Public Discussion
Date: 2005061602:01:04
Subject: Re:find formula for equation and answer

Turn the two fractions into one fraction and set numerator and
denominator equal to each other.  Solve the system.  

Like this  Given:  1/a +1/b = 37/180

Multiply 1/a by "b" and 1/b by "a" yielding  
               (a+b)/ ab =37/180

Set numerator and denominators equal to each other:

                a+b = 37   and  ab = 180  so,                         

Substitute into other equation: b + (180/b) = 37  
Multiplying by b and bringing everything to left 
b^2 -37b + 180 = 0   
Using quadratic formula:  b= (37 + sqr(649))/2 and
                          a= 37-((37 + sqr(649))/2 

The quad. almost factors so I wonder if there is an error in the
fraction 37/180

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