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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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