SOLUTION: If a-1/a=3 then find a^2+3a+1/a^2-3/a

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Question 1122043: If a-1/a=3 then find a^2+3a+1/a^2-3/a
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's ambiguous.
Add parentheses.

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
You are given


a - 1%2Fa = 3.


Square both sides.  You will get


9 = %28a+-+1%2Fa%29%5E2 = a%5E2 - 2a%2A%281%2Fa%29 + 1%2Fa%5E2 = a%5E2 - 2 + 1%2Fa%5E2.


Hence,  a%5E2 + 1%2Fa%5E2 = 9 + 2 = 11.


Then    a%5E2 + 3a + 1%2Fa%5E2 - 3%2Fa  (which is under the question) is equal to


    %28a%5E2+%2B+1%2Fa%5E2%29 + 3%2A%28a-1%2Fa%29 = 11 +3*3 = 20.


Answer.  Then  %28a%5E2+%2B+1%2Fa%5E2%29 + 3%2A%28a-1%2Fa%29 = 20.

Solved.

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To see many other similar solved problems, look into 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 online textbook under the topic "Evaluation, substitution".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.