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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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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)`
Posted by justaguide on July 3, 2013 at 4:41 AM (Answer #1)
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