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 abs(1/(sqrt((1-x^2)^2+(2*0.707*x)^2))-1) <0.01 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         abs ( 1 / ( sqrt ( ( 1 - x ^ 2 ) ^ 2 + ( 2 * 0.707 * x ) ^ 2 ) ) - 1 ) <0.01         (1)
        From the definition field of √
         ( 1 - x ^ 2 ) ^ 2 + ( 2 * 0.707 * x ) ^ 2 ≥ 0        (2 )
        From the definition field of divisor
         sqrt ( ( 1 - x ^ 2 ) ^ 2 + ( 2 * 0.707 * x ) ^ 2 ) ≠ 0        (3 )

    From inequality(1):
         -0.377882 < x < 0.377882
    From inequality(2):
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    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)
         -0.377882 < x < 0.377882     (4)
    From inequalities (3) and (4)
         -0.377882 < x < 0.377882     (5)

    The final solution set is :

         -0.377882 < x < 0.377882




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