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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 1 ≤√(2a－1)²＋(2a－2)² ≤3 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities：
        1 ≤ √ ( 2 * a - 1 ) ^ 2 + ( 2 * a - 2 ) ^ 2         (1)
         √ ( 2 * a - 1 ) ^ 2 + ( 2 * a - 2 ) ^ 2 ≤3         (2)
        From the definition field of √
         2 * x - 1 ≥ 0        (3 )

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    From inequality(1)：
         a ≤ 1/2 或  a ≥ 1
    From inequality(2)：
         a ≤ 3/2
    From inequality(3)：
         a ≥ 1/2

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    From inequalities (1) and (2)
         a ≤ 1/2 或  1 ≤ a ≤ 3/2    (4)
    From inequalities (3) and (4)
         1/2 ≤ a ≤ 1/2 或  1 ≤ a ≤ 3/2    (5)

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    The final solution set is :
         1/2 ≤ a ≤ 1/2 或  1 ≤ a ≤ 3/2

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