Question 1090815: x+1/x=2√6; x^8+x^4/x^4
Answer by ikleyn(52908)   (Show Source):
You can put this solution on YOUR website! .
If x+1/x=2√6  x^8+x^4/x^4.
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If x + 1/x =  then (squaring both sides)
 = 4*6 = 24, or
 +  +  = 24,
+ 2 + = 24 ====>
+ = 24 - 2 = 22.
Thus we have covered one half of the way and obtained THIS:
+ = 22. (1)
The second half is very similar. From (1) you have (by squaring both sides, again)
 =  = 484,
 +  +  = 484,
+ 2 + = 484 ====>
+ = 484 - 2 = 482.
Answer. If x + 1/x = then + = 482.
Solved.
For many other similar solved problems see the lesson
- HOW TO evaluate expressions involving  ,  and 
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".
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By the way, did you notice on how I edited your post at the very beginning of my response ?
It is commonly accepted in this forum to ask a question when you post your problem.
It is THE RULE of this forum, and it is the form of politeness in the same time.
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