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

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