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 1/10*{1+[1-(1-a)^10]*(186.89*a^2+54.23*a+12.8)/(17*a^2+5*a+2)} <1/6*{1+[1-(1-a)^6]*(24*a+10)/(2+3*a)} .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        1 / 10 * ( 1 + ( 1 - ( 1 - a ) ^ 10 ) * ( 186.89 * a ^ 2 + 54.23 * a + 12.8 ) / ( 17 * a ^ 2 + 5 * a + 2 ) ) <1 / 6 * ( 1 + ( 1 - ( 1 - a ) ^ 6 ) * ( 24 * a + 10 ) / ( 2 + 3 * a ) )         (1)
        From the definition field of divisor
         17 * x ^ 2 + 5 * x + 2 ≠ 0        (2 )
        From the definition field of divisor
         2 + 3 * x ≠ 0        (3 )

    From inequality(1):
         a < -0.711931 或  -0.666667 < a < 0.088275 或  0.158719 < a < 1.781492 或  a > 1.9776
    From inequality(2):
         a ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
    From inequality(3):
         a < -2/3 或  a > -2/3

    From inequalities (1) and (2)
         a < -0.711931 或  -0.666667 < a < 0.088275 或  0.158719 < a < 1.781492 或  a > 1.9776    (4)
    From inequalities (3) and (4)
         a < -0.711931 或  -2/3 < a < 0.088275 或  0.158719 < a < 1.781492 或  a > 1.9776    (5)

    The final solution set is :

         a < -0.711931 或  -2/3 < a < 0.088275 或  0.158719 < a < 1.781492 或  a > 1.9776




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