SOLUTION: If x^2+x-1=0 what is the value of x^4+(1/x^4)?

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Question 1118176: If x^2+x-1=0 what is the value of x^4+(1/x^4)?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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  x%5E4+%2B+1%2Fx%5E4 = %28x%5E2+%2B+1%2Fx%5E2%29%5E2-2 = Replace here x^2 with (1-x) since it is given = %28%28%281-x%29+%2B+1%2F%281-x%29%29%29%5E2 - 2 = 


= %28%28%281-x%29%5E2%2B1%29%2F%281-x%29%29%5E2 - 2 = %28%281-2x%2Bx%5E2+%2B+1%29%2F%281-x%29%29%5E2 - 2 = %28%282-2x%2Bx%5E2%29%2F%281-x%29%29%5E2 - 2 = %28%28%282-2x%29%2Bx%5E2%29%2F%281-x%29%29%5E2 - 2 = %28%282-2x%29%2F%281-x%29+%2B+x%5E2%2F%281-x%29%29%5E2 - 2 


= %282+%2B+x%5E2%2F%281-x%29%29%5E2 - 2 = replace x%5E2%2F%281-x%29 with 1, since  x%5E2 = (1-x) is given =


= %282%2B1%29%5E2 - 2 = 3%5E2-2 = 9 - 2 = 7.

Solved.