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Tough problem.

 

Evaluate a^3 + 1/(a^3) if a + 1/a = 6

 

Tell me if anything is unclear.

 Jun 22, 2017
 #1
avatar+98173 
+3

 

a^3  + 1/a^3     if  a  + 1/a  = 6

 

Note that   (a + 1/a)^2  =  a^2  + 2  +  1/a^2   = 36   →  a^2 + 1/a^2  =  34

 

And  a^3 + 1/a^3   can be factored as a sum of cubes thusly

 

(a  + 1/a)  ( a^2  -  1 +  1/a^2)  =

 

(6)  ([ a^2  + 1/a^2] - 1 )   =

 

(6) ( 34 - 1 )  =

 

6 * 33=

 

198

 

 

cool cool cool 

 

P.S. -  thanks to hectictar for spotting my earlier error...!!!!

 Jun 22, 2017
edited by CPhill  Jun 22, 2017

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