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☆1 inequalities
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Assignment:Find the solution set of inequality ln(1+x^2)+2x/(1+x^2) <0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
ln ( 1 + x ^ 2 ) + 2 * x / ( 1 + x ^ 2 ) <0 (1)
From the definition field of ln
1 + x ^ 2 > 0 (2 )
From the definition field of divisor
1 + x ^ 2 ≠ 0 (3 )
From inequality(1):
-1.280097 < x < 0
From inequality(2):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
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)
-1.280097 < x < 0 (4)
From inequalities (3) and (4)
-1.280097 < x < 0 (5)
The final solution set is :
-1.280097 < x < 0 Your problem has not been solved here? Please take a look at the hot problems !