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Assignment:Find the solution set of inequality e^(1-0.5x^(0.25))/(1+x^(0.125))
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
e ^ ( 1 - 0.5 * x ^ ( 0.25 ) ) / ( 1 + x ^ ( 0.125 ) ) < ln ( ( ln x / x ^ ( 0.5 ) ) ) (1)
From the definition field of divisor
1 + x ^ ( 0.125 ) ≠ 0 (2 )
From the definition field of ln
x > 0 (3 )
From the definition field of divisor
x ≠ 0 (4 )
From the definition field of ln
( ln x / x ^ ( 0.5 ) ) > 0 (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 ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequality(3):
x > 0
From inequality(4):
x < 0 或 x > 0
From inequality(5):
x > 1
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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