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Assignment:Find the solution set of inequality 2/3 <((4k-2)(k^2+1)^(1/2))/(2k^2+1) <3/4 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
2 / 3 < ( ( 4 * k - 2 ) * ( k ^ 2 + 1 ) ^ ( 1 / 2 ) ) / ( 2 * k ^ 2 + 1 ) (1)
( ( 4 * k - 2 ) * ( k ^ 2 + 1 ) ^ ( 1 / 2 ) ) / ( 2 * k ^ 2 + 1 ) <3 / 4 (2)
From the definition field of divisor
2 * x ^ 2 + 1 ≠ 0 (3 )
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):
k ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(3):
k ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
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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