SOLUTION: if x+1/x=3 then find the value of x^3+1/x^3

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Question 1049594: if x+1/x=3 then find the value of x^3+1/x^3
Answer by ikleyn(52748) About Me  (Show Source):
You can put this solution on YOUR website!
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if x+1/x=3 then find the value of x^3+1/x^3
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If x + 1%2Fx = 3 then 

27 = %28x+%2B+1%2Fx%29%5E3 = x%5E3 + 3%2Ax%5E2%2A%281%2Fx%29 + 3%2Ax%2A%281%2Fx%29%5E2 + 1 = x%5E3 + 3%2Ax + 3%2A%281%2Fx%29 + 1 = x%5E3 + 1%2Fx%5E3 + 3%2A%28x+%2B+1%2Fx%29 + 1.


Now replace the term  3%2A%28x+%2B+1%2Fx%29  before the last "1" by 3*3 = 9 (due to the condition !), and you will get

27 = x%5E3 + 1%2Fx%5E3 + 9 + 1.

And you need to make only one last step to get

x%5E3 + 1%2Fx%5E3  = 27 - 9 - 1 = 17.


Answer.  If x + 1%2Fx = 3 then  x%5E3 + 1%2Fx%5E3 = 17.

For other similar problems see the lesson
    - HOW TO evaluate expressions involving  %28x+%2B+1%2Fx%29,  %28x%5E2%2B1%2Fx%5E2%29  and  %28x%5E3%2B1%2Fx%5E3%29
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 lesson is the part of this textbook under the topic "Evaluation, substitution" of the section "Word problems".