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Simplify \(\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.\)

 Dec 18, 2019
 #1
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I have this problem too, could someone please help?

 Dec 18, 2019
 #2
avatar+109752 
+1

Note that  :

 

1^3  -  (3√3)^3 =   (  1 - 3√3)  ( 1  + 3√3  + (3√3)^2  )  =  ( 1 - 3√3)  ( 1 + 3√3 + 3√9 )  = ( 1 - 3)

 

So

 

 23√9

_______________           multiply  top/bottom by   (  1 - 3√3) 

( 1 + 3√3 + 3√9 )

 

 

23√9 (  1 - 3√3) 

____________________________   =

 (  1 - 3√3)  ( 1  + 3√3  + (3√3)^2  )

 

 

23√9  -  23√27

_____________   =

    1  -  3

 

23√27  - 23√9

____________    =

    3    -    1   

 

2 * 3 - 23√9

__________   =

          2

 

 

2  ( 3  - 3√9 )  

___________  = 

          2

 

3 - 3√9  =

 

3  - 32/3

 

 

 

cool cool cool

 Dec 18, 2019
 #3
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Is this simplified completely?

Guest Dec 18, 2019
 #4
avatar+109752 
0

Yep....simplified  completely....

 

 

cool cool cool

CPhill  Dec 18, 2019

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