SOLUTION: If x + 1/x = 3, then what is x^2 + 1/x^2?

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Question 1090595: If x + 1/x = 3, then what is x^2 + 1/x^2?
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
If  x + 1%2Fx = 3  then  (square both sides)

x%5E2 + 2%2Ax%2A%281%2Fx%29 + 1%2Fx%5E2 = 9,   or

x%5E2 + 2 + 1%2Fx%5E2 = 9,    which implies

x%5E2 + 1%2Fx%5E2 = 9 - 2 = 7.


Answer.  If  x + 1%2Fx = 3  then  x2 + 1%2Fx%5E2 = 9 - 2 = 7.

Solved.

Many similar problems solved and presented in 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.


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 online textbook under the topic  "Evaluation, substitution".