Mathematics
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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    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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