SOLUTION: Find the value of x^4+1/x^4 when x+1/x=2. Show solution without calculator

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Question 1133472: Find the value of x^4+1/x^4 when x+1/x=2. Show solution without calculator
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of
%28x%5E4%2B1%29%2Fx%5E4
when
%28x%2B1%29%2Fx=2
mult both sides by x
x + 1 = 2x
1 = 2x - x
x = 1
therefore
%28%281%5E4%29%2B1%29%2F1%5E4 = %281%2B1%29%2F1 = 2

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the value of x^4+1/x^4 when x+1/x=2. Show solution without calculator
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            See how I edited your post to give the problem the sense and the meaning as it should be. 

              Find the value of x%5E4 + 1%2Fx%5E4  when x + 1%2Fx = 2. Show solution without calculator.

Solution 

From   x + 1%2Fx = 2  you have  x%5E2 + 1 = 2x,  and then


    x%5E2+-+2x+%2B+1 = 0,

    %28x-1%29%5E2 = 0.


Hence,  x = 1.


Then  x%5E4 + 1%2Fx%5E4 = 1 + 1 = 2.

Solved.