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+(1-(1-a)^9)*(195*a*a+63*a+18)/(19*a*a+6*a+3))/9 <(1+(1-(1-a)^6)*(24*a+10)/(3*a+2))/6 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ( 1 + ( 1 - ( 1 - a ) ^ 9 ) * ( 195 * a * a + 63 * a + 18 ) / ( 19 * a * a + 6 * a + 3 ) ) / 9 < ( 1 + ( 1 - ( 1 - a ) ^ 6 ) * ( 24 * a + 10 ) / ( 3 * a + 2 ) ) / 6         (1)
        From the definition field of divisor
         19 * x * x + 6 * x + 3 ≠ 0        (2 )
        From the definition field of divisor
         3 * x + 2 ≠ 0        (3 )

    From inequality(1):
         a < -0.749406 或  -0.666667 < a < 1.658332
    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 < -0.749406 或  -0.666667 < a < 1.658332     (4)
    From inequalities (3) and (4)
         a < -0.749406 或  -2/3 < a < 1.658332     (5)

    The final solution set is :

         a < -0.749406 或  -2/3 < a < 1.658332




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