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