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 [1+(1-(1-a)^9)*(195*a^2+63*a+18)/(19*a^2+6*a+3)]×8/9×10^6 <[1+(1-(1-a)^6)*(23a+10)/(3a+2)]×8/6×10^6 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ( 1 + ( 1 - ( 1 - a ) ^ 9 ) * ( 195 * a ^ 2 + 63 * a + 18 ) / ( 19 * a ^ 2 + 6 * a + 3 ) ) × 8 / 9 × 10 ^ 6 < ( 1 + ( 1 - ( 1 - a ) ^ 6 ) * ( 23 * a + 10 ) / ( 3 * a + 2 ) ) × 8 / 6 × 10 ^ 6         (1)
        From the definition field of divisor
         19 * x ^ 2 + 6 * x + 3 ≠ 0        (2 )
        From the definition field of divisor
         3 * x + 2 ≠ 0        (3 )

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

    The final solution set is :

         a < -0.740888 或  -2/3 < a < 0.110039 或  0.189522 < a < 1.621958




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


Return