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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality 1/10*{1+[1-(1-a)^10]*(186.89*a^2+54.23*a+12.8)/(17*a^2+5*a+2)} <1/5*{1+[1-(1-a)^5]*(7.6*a+4.6)/(1+a)} .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
1 / 10 * ( 1 + ( 1 - ( 1 - a ) ^ 10 ) * ( 186.89 * a ^ 2 + 54.23 * a + 12.8 ) / ( 17 * a ^ 2 + 5 * a + 2 ) ) <1 / 5 * ( 1 + ( 1 - ( 1 - a ) ^ 5 ) * ( 7.6 * a + 4.6 ) / ( 1 + a ) ) (1)
From the definition field of divisor
17 * x ^ 2 + 5 * x + 2 ≠ 0 (2 )
From the definition field of divisor
1 + x ≠ 0 (3 )
From inequality(1):
a ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
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 < -1 或 a > -1
From inequalities (1) and (2)
a ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established! (4)
From inequalities (3) and (4)
a < -1 或 a > -1 (5)
The final solution set is :
a < -1 或 a > -1Your problem has not been solved here? Please take a look at the hot problems !