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

    From inequality(1):
         x ≤ 16/3
    From inequality(2):
         x > 9/4
    From inequality(3):
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!

    From inequalities (1) and (2)
         9/4 < x ≤ 16/3     (4)
    From inequalities (3) and (4)
         9/4 < x ≤ 16/3     (5)

    The final solution set is :

         9/4 < x ≤ 16/3




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