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☆1 inequalities
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Assignment:Find the solution set of inequality x(x+sqrt(x2+1))(x2+1)12+1(x+sqrt(x2+1)) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
x * ( x + sqrt ( x * 2 + 1 ) ) * ( x * 2 + 1 ) * 12 + 1 * ( x + sqrt ( x * 2 + 1 ) ) >0 (1)
From the definition field of √
x * 2 + 1 ≥ 0 (2 )
From the definition field of √
x * 2 + 1 ≥ 0 (3 )
From inequality(1):
x > -0.105662
From inequality(2):
x ≥ -1/2
From inequality(3):
x ≥ -1/2
From inequalities (1) and (2)
x > -0.105662 (4)
From inequalities (3) and (4)
x > -0.105662 (5)
The final solution set is :
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