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X^4-3X^2+1   solve ???

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mohamed90 | eNotes Newbie

Posted August 29, 2013 at 7:54 AM via web

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X^4-3X^2+1   solve ???

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llltkl | College Teacher | Valedictorian

Posted August 29, 2013 at 8:23 AM (Answer #1)

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`x^4-3x^2+1`

`=(x^2)^2-2*x^2*1+1^2-x^2`

`=(x^2-1)^2-x^2`

`=(x^2-1-x)(x^2-1+x)`

`={(x-1/2)^2-(sqrt5/2)^2}{(x+1/2)^2-(sqrt5/2)^2}`

`={(x-1/2-sqrt5/2)(x-1/2+sqrt5/2)}{(x+1/2-sqrt5/2) (x+1/2+sqrt5/2)}`

`={(x-(1/2+sqrt5/2))(x-(1/2-sqrt5/2))}{(x+(1/2-sqrt5/2))(x+(1/2+sqrt5/2))}`

To solve the system, put each term equal to zero.

The solutions are:

`x=(1/2+-sqrt5/2), (sqrt5/2-1/2), -(sqrt5/2+1/2)`

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