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Assignment:Find the solution set of inequality 0.9 <1/(((1-x^2)^2+(0.2*x)^2)^0.5) <1.1 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
0.9 <1 / ( ( ( 1 - x ^ 2 ) ^ 2 + ( 0.2 * x ) ^ 2 ) ^ 0.5 ) (1)
1 / ( ( ( 1 - x ^ 2 ) ^ 2 + ( 0.2 * x ) ^ 2 ) ^ 0.5 ) <1.1 (2)
From the definition field of divisor
( ( 1 - x ^ 2 ) ^ 2 + ( 0.2 * x ) ^ 2 ) ^ 0.5 ≠ 0 (3 )
From inequality(1):
-1.439842 < x < 1.439842
From inequality(2):
x < -1.366398 或 -0.304888 < x < 0.304888 或 x > 1.366398
From inequality(3):
x ∈ 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)
-1.439842 < x < -1.366398 或 -0.304888 < x < 0.304888 或 1.366398 < x < 1.439842 (4)
From inequalities (3) and (4)
-1.439842 < x < -1.366398 或 -0.304888 < x < 0.304888 或 1.366398 < x < 1.439842 (5)
The final solution set is :
-1.439842 < x < -1.366398 或 -0.304888 < x < 0.304888 或 1.366398 < x < 1.439842 Your problem has not been solved here? Please take a look at the hot problems !