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 1/6*{1+[1-(1-a)^6]*(23*a+10)/(3*a+2)} <1/9*{1+[1-(1-a)^9]*(195*a^2+63*a+18)/(19*a^2+6*a+3)} .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        1 / 6 * ( 1 + ( 1 - ( 1 - a ) ^ 6 ) * ( 23 * a + 10 ) / ( 3 * a + 2 ) ) <1 / 9 * ( 1 + ( 1 - ( 1 - a ) ^ 9 ) * ( 195 * a ^ 2 + 63 * a + 18 ) / ( 19 * a ^ 2 + 6 * a + 3 ) )         (1)
        From the definition field of divisor
         3 * x + 2 ≠ 0        (2 )
        From the definition field of divisor
         19 * x ^ 2 + 6 * x + 3 ≠ 0        (3 )

    From inequality(1):
         -0.740888 < a < -0.666667 或  0.110039 < a < 0.189522 或  a > 1.621958
    From inequality(2):
         a < -2/3 或  a > -2/3
    From inequality(3):
         a ∈ 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)
         -0.740888 < a < -0.666667 或  0.110039 < a < 0.189522 或  a > 1.621958    (4)
    From inequalities (3) and (4)
         -0.740888 < a < -0.666667 或  0.110039 < a < 0.189522 或  a > 1.621958    (5)

    The final solution set is :

         -0.740888 < a < -0.666667 或  0.110039 < a < 0.189522 或  a > 1.621958




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