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Assignment:Find the solution set of inequality sqrt(t+sqrt(t^3)) <= t .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( t + sqrt ( t ^ 3 ) ) <= t (1)
From the definition field of √
x ^ 3 ≥ 0 (2 )
From the definition field of √
x + sqrt ( x ^ 3 ) ≥ 0 (3 )
From inequality(1):
t ≤ 0 或 t ≥ 2.618034
From inequality(2):
t ≥ 0
From inequality(3):
t ≥ 0
From inequalities (1) and (2)
0 ≤ t ≤ 0 或 t ≥ 2.618034 (4)
From inequalities (3) and (4)
0 ≤ t ≤ 0 或 t ≥ 2.618034 (5)
The final solution set is :
0 ≤ t ≤ 0 或 t ≥ 2.618034Your problem has not been solved here? Please take a look at the hot problems !