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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 50^2+x^2-2*50*x*cos(180-arcsin((50*sin50)/x-50)) >(x+15)^2 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        50 ^ 2 + x ^ 2 - 2 * 50 * x * cos ( 180 - arcsin ( ( 50 * sin 50 ) / x - 50 ) ) > ( x + 15 ) ^ 2         (1)
        From the definition field of divisor
        x ≠ 0        (2 )
        From the definition field of arcsin
         ( 50 * sin 50 ) / x - 50 ≥ -1        (3 )
         ( 50 * sin 50 ) / x - 50 ≤ 1        (4 )

    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 或  x > 0
    From inequality(3):
         -0.267729 ≤ x ≤ 0
    From inequality(4):
         x ≤ -0.25723 或  x ≥ 0

    From inequalities (1) and (2)
         x < 0 或  x > 0    (5)
    From inequalities (3) and (5)
         -0.267729 ≤ x < 0    (6)
    From inequalities (4) and (6)
         -0.267729 ≤ x ≤ -0.25723    (7)

    The final solution set is :

         -0.267729 ≤ x ≤ -0.25723

    *Note: Radian.



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