Mathematics
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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 0.5(x+(1+4xx)^-0.5)*((4(x+(1+4xx)^-0.5)^2)+1)^0.5+0.25*ln(2x+2(1+4xx)^-0.5+(1+4(x+(1+4xx)^-0.5)^2)^0.5-1.5 ) <= 1.3((50-xx-1/(4xx+1))^2+xx)^0.5 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        0.5 * ( x + ( 1 + 4 * x * x ) ^ -0.5 ) * ( ( 4 * ( x + ( 1 + 4 * x * x ) ^ -0.5 ) ^ 2 ) + 1 ) ^ 0.5 + 0.25 * ln ( 2 * x + 2 * ( 1 + 4 * x * x ) ^ -0.5 + ( 1 + 4 * ( x + ( 1 + 4 * x * x ) ^ -0.5 ) ^ 2 ) ^ 0.5 - 1.5 ) <= 1.3 * ( ( 50 - x * x - 1 / ( 4 * x * x + 1 ) ) ^ 2 + x * x ) ^ 0.5         (1)
        From the definition field of ln
         2 * x + 2 * ( 1 + 4 * x * x ) ^ -0.5 + ( 1 + 4 * ( x + ( 1 + 4 * x * x ) ^ -0.5 ) ^ 2 ) ^ 0.5 - 1.5 > 0        (2 )
        From the definition field of divisor
         4 * x * x + 1 ≠ 0        (3 )

    From inequality(1):
         x ≤ 5.271438 或  x ≥ 14.866204
    From inequality(2):
         x > -0.499282
    From inequality(3):
         x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!

    From inequalities (1) and (2)
         -0.499282 < x ≤ 5.271438 或  x ≥ 14.866204    (4)
    From inequalities (3) and (4)
         -0.499282 < x ≤ 5.271438 或  x ≥ 14.866204    (5)

    The final solution set is :

         -0.499282 < x ≤ 5.271438 或  x ≥ 14.866204




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