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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 6x(100+xx)^2 ≤(sqrt(100+xx))^3-x(100+xx)^2 <8x(100+xx)^2 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities：
        6 * x * ( 100 + x * x ) ^ 2 ≤ ( sqrt ( 100 + x * x ) ) ^ 3 - x * ( 100 + x * x ) ^ 2         (1)
         ( sqrt ( 100 + x * x ) ) ^ 3 - x * ( 100 + x * x ) ^ 2 <8 * x * ( 100 + x * x ) ^ 2         (2)
        From the definition field of √
         100 + x * x ≥ 0        (3 )

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    From inequality(1)：
         x ≤ 0.014286
    From inequality(2)：
         x ＞ 0.011111
    From inequality(3)：
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!

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    From inequalities (1) and (2)
         0.011111 < x ≤ 0.014286     (4)
    From inequalities (3) and (4)
         0.011111 < x ≤ 0.014286     (5)

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    The final solution set is :
         0.011111 < x ≤ 0.014286

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