SOLUTION: Find the value of x^4+1/x^4 when x+1/x=2.Show solution without calculator 2 4 8 16

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Find the value of x^4+1/x^4 when x+1/x=2.Show solution without calculator 2 4 8 16      Log On


   

Question 1133481: Find the value of x^4+1/x^4 when x+1/x=2.Show solution without calculator
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Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The easiest way is just to solve x%2B1%2Fx=2 for x
and substitute in x%5E4%2B1%2Fx%5E4

x%2B1%2Fx=2

Multiply through by x

x%5E2%2Bx%2Fx=2x

x%5E2%2B1=2x

x%5E2-2x%2B1=0

%28x-1%29%28x-1%29=0

x-1=0

x=1

Substitute in 

x%5E4%2B1%5E%22%22%2Fx%5E4

1%2B1%5E%22%22%2F1

1%2B1

2

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But maybe you meant "without solving for x". If so, then:

x%2B1%2Fx=2

Square both sides:

%28x%2B1%2Fx%29%5E2=2%5E2

x%5E2%2B2%28x%29%281%2Fx%5E%22%22%29%2B1%2Fx%5E2=4

x%5E2%2B2%2B1%2Fx%5E2=4

x%5E2%2B1%2Fx%5E2=2

Square both sides:

%28x%5E2%2B1%2Fx%5E2%29%5E2=2%5E2

x%5E4%2B2%28x%5E2%29%281%2Fx%5E2%29%2B1%2Fx%5E4=4

x%5E4%2B2%2B1%2Fx%5E4=4

x%5E4%2B1%2Fx%5E4=2

That was done without solving for x.

Edwin