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 e{(lnx/sqrtx)+(lnx/(x^(1/8)))}-1 >1-e{lnx/sqrtx-lnx/(x^(1/8))} .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         e ( ( ln x / sqrt x ) + ( ln x / ( x ^ ( 1 / 8 ) ) ) ) - 1 >1 - e ( ln x / sqrt x - ln x / ( x ^ ( 1 / 8 ) ) )         (1)
        From the definition field of ln
        x > 0        (2 )
        From the definition field of √
        x ≥ 0        (3 )
        From the definition field of ln
        x > 0        (4 )
        From the definition field of divisor
         x ^ ( 1 / 8 ) ≠ 0        (5 )
        From the definition field of ln
        x > 0        (6 )
        From the definition field of √
        x ≥ 0        (7 )
        From the definition field of ln
        x > 0        (8 )
        From the definition field of divisor
         x ^ ( 1 / 8 ) ≠ 0        (9 )

    From inequality(1):
         x > 1
    From inequality(2):
         x > 0
    From inequality(3):
         x ≥ 0
    From inequality(4):
         x > 0
    From inequality(5):
         x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
    From inequality(6):
         x > 0
    From inequality(7):
         x ≥ 0
    From inequality(8):
         x > 0
    From inequality(9):
         x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!

    From inequalities (1) and (2)
         x > 1    (10)
    From inequalities (3) and (10)
         x > 1    (11)
    From inequalities (4) and (11)
         x > 1    (12)
    From inequalities (5) and (12)
         x > 1    (13)
    From inequalities (6) and (13)
         x > 1    (14)
    From inequalities (7) and (14)
         x > 1    (15)
    From inequalities (8) and (15)
         x > 1    (16)
    From inequalities (9) and (16)
         x > 1    (17)

    The final solution set is :

         x > 1




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


Return