Mathematics
语言:中文
Language:English

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 1/(1+x^(1/2)) <= lnx/sqrt(x) .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        1 / ( 1 + x ^ ( 1 / 2 ) ) <= ln x / sqrt ( x )         (1)
        From the definition field of divisor
         1 + x ^ ( 1 / 2 ) ≠ 0        (2 )
        From the definition field of ln
        x > 0        (3 )
        From the definition field of √
         x ≥ 0        (4 )

    From inequality(1):
         x ≥ 1.769823
    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

    From inequalities (1) and (2)
         x ≥ 1.769823    (5)
    From inequalities (3) and (5)
         x ≥ 1.769823    (6)
    From inequalities (4) and (6)
         x ≥ 1.769823    (7)

    The final solution set is :

         x ≥ 1.769823




Your problem has not been solved here? Please take a look at the  hot problems !


Return