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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 4*x^2/(1-sqrt(1+2*x))^2 <2x+9 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        4 * x ^ 2 / ( 1 - sqrt ( 1 + 2 * x ) ) ^ 2 <2 * x + 9         (1)
        From the definition field of √
         1 + 2 * x ≥ 0        (2 )
        From the definition field of divisor
         1 - sqrt ( 1 + 2 * x ) ≠ 0        (3 )

    From inequality(1):
         x < 45/8
    From inequality(2):
         x ≥ -1/2
    From inequality(3):
         x < 0 或  x > 0

    From inequalities (1) and (2)
         -1/2 ≤ x < 45/8    (4)
    From inequalities (3) and (4)
         -1/2 ≤ x < 0 或  0 < x < 45/8     (5)

    The final solution set is :

         -1/2 ≤ x < 0 或  0 < x < 45/8




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