SOLUTION: If (x+(1/x))^2 = 7 and x is a positive real number, find the exact value of x^3 + 1/x^3 Thank you!

Question 1086530: If (x+(1/x))^2 = 7 and x is a positive real number, find the exact value of x^3 + 1/x^3
Thank you!
Answer by ikleyn(52863) (Show Source): You can put this solution on YOUR website!
.

1.  From   = 7  you have   = .


2.  It implies 

     =  =  =  +  =  +  =  + .


    Now replace in the last term    by    (based on n.1),  and you will get

     =  + ,   or


     = .

Answer. = .

Solved.

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