Mathematics
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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 (-3a-sqrt((3a)^2-4*(-2a)*(a-2)))/(2*(-2a)) >0 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ( -3 * a - sqrt ( ( 3 * a ) ^ 2 - 4 * ( -2 * a ) * ( a - 2 ) ) ) / ( 2 * ( -2 * a ) ) >0         (1)
        From the definition field of √
         ( 3 * x ) ^ 2 - 4 * ( -2 * x ) * ( x - 2 ) ≥ 0        (2 )
        From the definition field of divisor
         2 * ( -2 * x ) ≠ 0        (3 )

    From inequality(1):
         a ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(2):
         a ≤ 0 或  a ≥ 0.941176
    From inequality(3):
         a < 0 或  a > 0

    From inequalities (1) and (2)
         a ≤ 0 或  a ≥ 0.941176    (4)
    From inequalities (3) and (4)
         a < 0 或  a ≥ 0.941176    (5)

    The final solution set is :

         a < 0 或  a ≥ 0.941176




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