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Assignment:Find the solution set of inequality 4x^2/(x^2+1)^2-2x/(x^2+1)^2-2/(x^2+1) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
4 * x ^ 2 / ( x ^ 2 + 1 ) ^ 2 - 2 * x / ( x ^ 2 + 1 ) ^ 2 - 2 / ( x ^ 2 + 1 ) >0 (1)
From the definition field of divisor
x ^ 2 + 1 ≠ 0 (2 )
From the definition field of divisor
x ^ 2 + 1 ≠ 0 (3 )
From the definition field of divisor
x ^ 2 + 1 ≠ 0 (4 )
From inequality(1):
x < -0.618034 或 x > 1.618034
From inequality(2):
x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
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 inequality(4):
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)
x < -0.618034 或 x > 1.618034 (5)
From inequalities (3) and (5)
x < -0.618034 或 x > 1.618034 (6)
From inequalities (4) and (6)
x < -0.618034 或 x > 1.618034 (7)
The final solution set is :
x < -0.618034 或 x > 1.618034Your problem has not been solved here? Please take a look at the hot problems !