SOLUTION: If x-1/x =4, find the value of x^3-1/x^3 and x^4+1/x^4 Thank you!

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Question 1082554: If x-1/x =4, find the value of x^3-1/x^3 and x^4+1/x^4
Thank you!
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
x-1%2Fx+=4, find the value of x%5E3-1%2Fx%5E3 and x%5E4%2B1%2Fx%5E4

x-1%2Fx+=4

Square both sides:

x%5E2-2%28x%29%281%2Fx%29%2B1%2Fx%5E2=16

x%5E2-2%2B1%2Fx%5E2+=16

x%5E2%2B1%2Fx%5E2+=18   <-- the answer to 1st expression

Square both sides again

x%5E4%2B2x%5E2%281%2Fx%5E2%29%2B1%2Fx%5E4=324

x%5E4%2B2%2B1%2Fx%5E4+=324

x%5E4%2B1%2Fx%5E4+=322  <-- the answer to 3rd expression

For the 2nd expression, take the two equations:

x-1%2Fx+=4 and x%5E2%2B1%2Fx%5E2+=18

Multiply equals by equals:

%28x-1%2Fx%29%28x%5E2%2B1%2Fx%5E2%29+=+%284%29%2818%29

x%5E3%2Bx%281%2Fx%5E2%29-%281%2Fx%29%28x%5E2%29-1%2Fx%5E3=72

x%5E3%2B1%2Fx-x-1%2Fx%5E3=72

x%5E3-1%2Fx%5E3=72%2Bx-1%2Fx

x%5E3-1%2Fx%5E3=72%2B%28x-1%2Fx%29, and since x-1%2Fx+=4,

x%5E3-1%2Fx%5E3=72%2B4

x%5E3-1%2Fx%5E3=76 <-- answer to 2nd expression

Edwin