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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 sqrt(x^2-3*x+1)+sqrt(2*x^2+2x*-5)     Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         sqrt ( x ^ 2 - 3 * x + 1 ) + sqrt ( 2 * x ^ 2 + 2 * x * -5 ) < sqrt ( 3 * x ^ 2 + 7 * x - 11 ) + sqrt ( 7 - 8 * x )         (1)
        From the definition field of √
         x ^ 2 - 3 * x + 1 ≥ 0        (2 )
        From the definition field of √
         2 * x ^ 2 + 2 * x * -5 ≥ 0        (3 )
        From the definition field of √
         3 * x ^ 2 + 7 * x - 11 ≥ 0        (4 )
        From the definition field of √
         7 - 8 * x ≥ 0        (5 )

    From inequality(1):
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(2):
         x ≤ 0.381966 或  x ≥ 2.618034
    From inequality(3):
         x ≤ 0 或  x ≥ 5
    From inequality(4):
         x ≤ -3.408937 或  x ≥ 1.075604
    From inequality(5):
         x ≤ 7/8

    From inequalities (1) and (2)
         x ≤ 0.381966 或  x ≥ 2.618034    (6)
    From inequalities (3) and (6)
         x ≤ 0 或  x ≥ 5    (7)
    From inequalities (4) and (7)
         x ≤ -3.408937 或  x ≥ 5    (8)
    From inequalities (5) and (8)
         x ≤ -3.408937    (9)

    The final solution set is :

         x ≤ -3.408937




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