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If x+1/x=-5 what is x^3+1/(x^3)?

Guest Aug 5, 2017
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x+1/x = -5 what is x^3+1/(x^3)

 

If  x + 1/x   = -5  then squaring both sides, we have that

(x + 1/x)^2  = 25  →  x^2 + 2 + 1/x^2  = 25  →  x^2 + 1/x^2  = 23

 

Note that  x^3  + 1/ (x^3)   can be factored as  a sum of cubes thusly :

 

(x + 1/x) ( x^2 - x(1/x) + 1/x^2 )  =

 

(x + 1/x)  ( x^2  - 1  + 1/x^2 )  =

 

(x  + 1/x) ( x^2 + 1/x^2  - 1 )     substituting

 

( -5)  (  23  - 1 )  =

 

(-5) (22)  = 

 

-110

 

 

cool cool cool

CPhill  Aug 5, 2017

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