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-1
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avatar+1405 

Help me Please.

 

Roots: find the square roots of the following polynomials.

 

4x2/y2 - 36x/y + 81

 Feb 1, 2018
 #1
avatar+95872 
+1

OK.....this looks a little daunting.....let's make it easier

 

Let     x /y  =  "a"

So     x^2 / y^2  =  (x /y)^2   =  "a^2"

 

Now.....we have someting that is a little more familiar....so....

 

4 (x^2/y^2)   - 36 (x/y)  + 81        becomes

 

4a^2  -  36a  + 81        let us guess that the factorization of this is

 

(2a - 9) (2a - 9)          verify for yourself that this is the correct factoring

 

(2a - 9)^2

 

But.....also ....notice that   

 

[ -(2a - 9) ]  [ - (2a - 9) ]    will also produce the same result  = [ - (2a - 9) ]^2

 

So......the square roots  are

 

±(2a - 9)       ....so....just back-substitute and we have

 

± [ 2(x/y) - 9 ]

 

 

 

cool cool cool

 Feb 1, 2018

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