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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 0 <(4x^2+1)/(x^2-x+1) <3 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        0 < ( 4 * x ^ 2 + 1 ) / ( x ^ 2 - x + 1 )         (1)
         ( 4 * x ^ 2 + 1 ) / ( x ^ 2 - x + 1 ) <3         (2)
        From the definition field of divisor
         x ^ 2 - x + 1 ≠ 0        (3 )

    From inequality(1):
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(2):
         -3.561553 < x < 0.561553
    From inequality(3):
         x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!

    From inequalities (1) and (2)
         -3.561553 < x < 0.561553     (4)
    From inequalities (3) and (4)
         -3.561553 < x < 0.561553     (5)

    The final solution set is :

         -3.561553 < x < 0.561553




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