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Solve the inequality 1 + 2x + 2x^2 - x^4 < 0 The problem is that x^4 - 2x^2 - 2x -1...

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askjdbashdiua | eNotes Newbie

Posted July 3, 2013 at 3:37 AM via web

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Solve the inequality 1 + 2x + 2x^2 - x^4 < 0

The problem is that x^4 - 2x^2 - 2x -1 cannot be factored.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 3, 2013 at 4:41 AM (Answer #1)

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The inequality 1 + 2x + 2x^2 - x^4 < 0 has to be solved.

1 + 2x + 2x^2 - x^4 < 0

=> -(x+1)*(x^3-x^2-x-1) < 0

=> (x+1)*(x^3-x^2-x-1) > 0

This is true when x + 1 > 0 and x^3-x^2-x-1 > 0 or when x + 1 < 0 and x^3-x^2-x-1 < 0

The expression x^3-x^2-x-1 cannot be factored. The cubic equation has one real root that is approximately 1.8399

The inequality reduces to an approximate form : (x+1)(x - 1.7675) > 0

=> x < -1 and x > 1.8393

The solution of the inequality is `(-oo, -1)U(1.8393, oo)`

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