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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 1 <= sqrt(x^2+4*x+9-12*x) <= 3 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        1 <= sqrt ( x ^ 2 + 4 * x + 9 - 12 * x )         (1)
         sqrt ( x ^ 2 + 4 * x + 9 - 12 * x ) <= 3         (2)
        From the definition field of √
         x ^ 2 + 4 * x + 9 - 12 * x ≥ 0        (3 )

    From inequality(1):
         x ≤ 1.171573 或  x ≥ 6.828427
    From inequality(2):
         0 ≤ x ≤ 8
    From inequality(3):
         x ≤ 1.354249 或  x ≥ 6.645751

    From inequalities (1) and (2)
         0 ≤ x ≤ 1.171573 或  6.828427 ≤ x ≤ 8    (4)
    From inequalities (3) and (4)
         0 ≤ x ≤ 1.171573 或  6.828427 ≤ x ≤ 8    (5)

    The final solution set is :

         0 ≤ x ≤ 1.171573 或  6.828427 ≤ x ≤ 8




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