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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 sqrt(r^2+200r+10000-400)-sqrt(r^2-200r+10000-400) >2r .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         sqrt ( r ^ 2 + 200 * r + 10000 - 400 ) - sqrt ( r ^ 2 - 200 * r + 10000 - 400 ) >2 * r         (1)
        From the definition field of √
         x ^ 2 + 200 * x + 10000 - 400 ≥ 0        (2 )
        From the definition field of √
         x ^ 2 - 200 * x + 10000 - 400 ≥ 0        (3 )

    From inequality(1):
         r > 0
    From inequality(2):
         r ≤ -120 或  r ≥ -80
    From inequality(3):
         r ≤ 80 或  r ≥ 120

    From inequalities (1) and (2)
         r > 0    (4)
    From inequalities (3) and (4)
         0 < r ≤ 80 或  r ≥ 120    (5)

    The final solution set is :

         0 < r ≤ 80 或  r ≥ 120




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