SOLUTION: if x + 1/x = 6, find the value of x^2 + 1/x^2.

Algebra ->  Equations -> SOLUTION: if x + 1/x = 6, find the value of x^2 + 1/x^2.      Log On


   

Question 1118373: if x + 1/x = 6, find the value of x^2 + 1/x^2.
Found 3 solutions by HEY654321, ikleyn, MathTherapy:
Answer by HEY654321(7) About Me  (Show Source):
You can put this solution on YOUR website!
Square x + 1/x = 6 and you should get your answer of 34.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
if x + 1/x = 6, find the value of x^2 + 1/x^2.
~~~~~~~~~~~~~~~~~~~~~~~~~ 

if  x+%2B+1%2Fx = 6,  then,  squaring both sides, you have


x%5E2 + 2%2Ax%2A%281%2Fx%29%29 + 1%2Fx%5E2 = 36,   or


x%5E2 + 1%2Fx%5E2 = 36 - 2 = 34.

The solution is completed.


The major lesson to learn from this solution is THIS: 

    you do not need to solve the original equation explicitly to get the answer.

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You can find many other similar solved problems in 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

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.



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

if x + 1/x = 6, find the value of x^2 + 1/x^2.
Another tutor and I did this a few days ago. Why're you posting it again? 

The 2 different solutions were not enough?