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Assignment:Find the solution set of inequality 6(100+xx)^2 ≤(sqrt(100+xx))^3-x(100+xx)^2 <8(100+xx)^2 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
6 * ( 100 + x * x ) ^ 2 ≤ ( sqrt ( 100 + x * x ) ) ^ 3 - x * ( 100 + x * x ) ^ 2 (1)
( sqrt ( 100 + x * x ) ) ^ 3 - x * ( 100 + x * x ) ^ 2 <8 * ( 100 + x * x ) ^ 2 (2)
From the definition field of √
100 + x * x ≥ 0 (3 )
From inequality(1):
x ≤ -5.913926
From inequality(2):
x > -7.921614
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)
-7.921614 < x ≤ -5.913926 (4)
From inequalities (3) and (4)
-7.921614 < x ≤ -5.913926 (5)
The final solution set is :
-7.921614 < x ≤ -5.913926 Your problem has not been solved here? Please take a look at the hot problems !