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 100/(1+(x-1)^1.2) <(2.5*(sqrt(2*x+0.25)-0.5))/x .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        100 / ( 1 + ( x - 1 ) ^ 1.2 ) < ( 2.5 * ( sqrt ( 2 * x + 0.25 ) - 0.5 ) ) / x         (1)
        From the definition field of divisor
         1 + ( x - 1 ) ^ 1.2 ≠ 0        (2 )
        From the definition field of √
         2 * x + 0.25 ≥ 0        (3 )
        From the definition field of divisor
        x ≠ 0        (4 )

    From inequality(1):
         x > 125.11639
    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 ≥ -1/8
    From inequality(4):
         x < 0 或  x > 0

    From inequalities (1) and (2)
         x > 125.11639    (5)
    From inequalities (3) and (5)
         x > 125.11639    (6)
    From inequalities (4) and (6)
         x > 125.11639    (7)

    The final solution set is :

         x > 125.11639




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


Return