SOLUTION: x+5 + 1/x+1 = 6 then find the value of (x+1)^3 + 1/(x+1)^3

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Question 1087960: x+5 + 1/x+1 = 6 then find the value of (x+1)^3 + 1/(x+1)^3
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
If   x%2B5+%2B+1%2F%28x%2B1%29 = 6 then 

    x%2B1+%2B+1%2F%28x%2B1%29 = 6 - 4 = 2,

and the equivalent question is:


If a+%2B+1%2Fa = 2, then find the value of a%5E3+%2B+1%2Fa%5E3.


I solved such problems MANY TIMES in this forum, and just tired of it.


See the lesson

    - HOW TO evaluate expressions involving  %28x+%2B+1%2Fx%29,  %28x%5E2%2B1%2Fx%5E2%29,  %28x%5E3+%2B+1%2Fx%5E3%29   and  %28x%5E5%2B1%2Fx%5E5%29 

in this site, and find full solution there (Problem 2), as well as many other relevant hings.


Closely related to it are the lessons
    - Advanced lesson on evaluating expressions
    - HOW TO evaluate functions of roots of a square equation
    - HOW TO evaluate functions of roots of a cubic and quartic equation
    - Advanced problems on Vieta's formulas
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Evaluation, substitution".