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 > 1.621958Your problem has not been solved here? Please take a look at the hot problems !