Mathematics
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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 2 questions will be solved this time.Among them
           ☆2 inequalities

[ 1/2Inequality]
    Assignment:Find the solution set of inequality 0 <(a+13-sqrt((a+13)*(a+13)-28(a*a-a-2)))/2 <1 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        0 < ( a + 13 - sqrt ( ( a + 13 ) * ( a + 13 ) - 28 * ( a * a - a - 2 ) ) ) / 2         (1)
         ( a + 13 - sqrt ( ( a + 13 ) * ( a + 13 ) - 28 * ( a * a - a - 2 ) ) ) / 2 <1         (2)
        From the definition field of √
         ( x + 13 ) * ( x + 13 ) - 28 * ( x * x - x - 2 ) ≥ 0        (3 )

    From inequality(1):
         a < -1 或  a > 2
    From inequality(2):
         -1.43875 < a < 2.581607
    From inequality(3):
         -2.05505 ≤ a ≤ 4.05505

    From inequalities (1) and (2)
         -1.43875 < a < -1 或  2 < a < 2.581607     (4)
    From inequalities (3) and (4)
         -1.43875 < a < -1 或  2 < a < 2.581607     (5)

    The final solution set is :

         -1.43875 < a < -1 或  2 < a < 2.581607

[ 2/2Inequality]
    Assignment:Find the solution set of inequality 1 <(a+13+sqrt((a+13)*(a+13)-28(a*a-a-2)))/2 <2 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        1 < ( a + 13 + sqrt ( ( a + 13 ) * ( a + 13 ) - 28 * ( a * a - a - 2 ) ) ) / 2         (1)
         ( a + 13 + sqrt ( ( a + 13 ) * ( a + 13 ) - 28 * ( a * a - a - 2 ) ) ) / 2 <2         (2)
        From the definition field of √
         ( x + 13 ) * ( x + 13 ) - 28 * ( x * x - x - 2 ) ≥ 0        (3 )

    From inequality(1):
         a > -2.10848
    From inequality(2):
         a < -2.096613
    From inequality(3):
         -2.05505 ≤ a ≤ 4.05505

    From inequalities (1) and (2)
         -2.10848 < a < -2.096613     (4)
    From inequalities (3) and (4)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (5)

    The final solution set is :

        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!




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