SOLUTION: What is the difference of the factors of the expression x^2 + (1/x^2) – 6?

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Question 1092954: What is the difference of the factors of the expression x^2 + (1/x^2) – 6?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + (1/x^2) – 6 =
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(x^4 + 1 -6x^2) / x^2 =
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(x^2 -2x - 1)(x^2 +2x - 1) / x^2
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((-x + sqrt(2) - 1) (-x + sqrt(2) + 1) (x + sqrt(2) - 1) (x + sqrt(2) + 1))/x^2
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-x + sqrt(2) - 1 + x - sqrt(2) - 1 = -2
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-x + sqrt(2) - 1 - x - sqrt(2) + 1 = -2x
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-x + sqrt(2) - 1 -x - sqrt(2) - 1 = -2x - 2
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-x + sqrt(2) + 1 + x - sqrt(2) + 1 = 2
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-x + sqrt(2) + 1 - x - sqrt(2) + 1 = -2x + 2
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-x + sqrt(2) + 1 - x - sqrt(2) - 1 = -2x
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