SOLUTION: (x-1/x)=5 ,then what is the value of (x^4+1/x^4)=?

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Question 1128761: (x-1/x)=5 ,then what is the value of (x^4+1/x^4)=?
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
If  

x+-+1%2Fx = 5,                     (1)

then after squaring both sides


x%5E2 - 2%2Ax%2A%281%2Fx%29 + 1%2Fx%5E2 = 25,

x%5E2 - 2 + 1%2Fx%5E2 = 25,

x%5E2 + 1%2Fx%5E2 = 25 + 2 = 27.       (2)


Now square (2) again (both sides). You will get


x%5E4 + 2%2Ax%5E2%2A%281%2Fx%5E2%29 + 1%2Fx%5E4 = 27%5E2

x%5E4 + 1%2Fx%5E4 = 27%5E2-2

x%5E4 + 1%2Fx%5E4 = 727.     ANSWER

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To see many other similar solved problems, look into the lessons
    - HOW TO evaluate expressions involving  %28x+%2B+1%2Fx%29,  %28x%5E2%2B1%2Fx%5E2%29  and  %28x%5E3%2B1%2Fx%5E3%29
    - Advanced lesson on evaluating expressions
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 lessons are 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.