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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality (1+1-(1-a)^9*(117*a*a+261*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 * ( 117 * a * a + 261 * 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 < -2.292423 或 -0.050205 < a < 1.902498
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 < -2.292423 或 -0.050205 < a < 1.902498 (4)
From inequalities (3) and (4)
a < -2.292423 或 -0.050205 < a < 1.902498 (5)
The final solution set is :
a < -2.292423 或 -0.050205 < a < 1.902498 Your problem has not been solved here? Please take a look at the hot problems !