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