Mathematics
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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 2 questions will be solved this time.Among them
           ☆2 inequalities

[ 1/2Inequality]
    Assignment:Find the solution set of inequality sqrt(766.237761-x*x)-sqrt(766.237761-(x+0.1)*(x+0.1)) >1 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         sqrt ( 766.237761 - x * x ) - sqrt ( 766.237761 - ( x + 0.1 ) * ( x + 0.1 ) ) >1         (1)
        From the definition field of √
         766.237761 - x * x ≥ 0        (2 )
        From the definition field of √
         766.237761 - ( x + 0.1 ) * ( x + 0.1 ) ≥ 0        (3 )

    From inequality(1):
         x > 27.489086
    From inequality(2):
         -27681/1000 ≤ x ≤ 27681/1000
    From inequality(3):
         -27781/1000 ≤ x ≤ 27581/1000

    From inequalities (1) and (2)
         27.489086 < x ≤ 27681/1000     (4)
    From inequalities (3) and (4)
         27.489086 < x ≤ 27581/1000     (5)

    The final solution set is :

         27.489086 < x ≤ 27581/1000

[ 2/2Inequality]
    Assignment:Find the solution set of inequality arcsin((x+0.1)/27.6881)-arcsin(x/27.6881) >1 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         arcsin ( ( x + 0.1 ) / 27.6881 ) - arcsin ( x / 27.6881 ) >1         (1)
        From the definition field of arcsin
         ( x + 0.1 ) / 27.6881 ≥ -1        (2 )
         ( x + 0.1 ) / 27.6881 ≤ 1        (3 )
        From the definition field of arcsin
         x / 27.6881 ≥ -1        (4 )
         x / 27.6881 ≤ 1        (5 )

    From inequality(1):
        The solution set is empty, that is, within the range of real numbers, the inequality will never be established!
    From inequality(2):
         x ≥ -277881/10000
    From inequality(3):
         x ≤ 275881/10000
    From inequality(4):
         x ≥ -276881/10000
    From inequality(5):
         x ≤ 276881/10000

    The final solution set is :

        The solution set is empty,that is, the inequality will never be estatlished within the real number range.




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