Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality √{{k+√[k^2+(sin54)^2-2*k*(sin54)^2]}^2+k^2-2*k*{k+√[k^2+(sin54)^2-2*k*(sin54)^2]*cos72}}     Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality：
         √ ( ( k + √ ( k ^ 2 + ( sin 54 ) ^ 2 - 2 * k * ( sin 54 ) ^ 2 ) ) ^ 2 + k ^ 2 - 2 * k * ( k + √ ( k ^ 2 + ( sin 54 ) ^ 2 - 2 * k * ( sin 54 ) ^ 2 ) * cos 72 ) ) < cos 54 + 1 - k         (1)
        From the definition field of √
         x ^ 2 + ( sin 54 ) ^ 2 - 2 * x * ( sin 54 ) ^ 2 ≥ 0        (2 )
        From the definition field of √
         x ^ 2 + ( sin 54 ) ^ 2 - 2 * x * ( sin 54 ) ^ 2 ≥ 0        (3 )
        From the definition field of √
         ( x + √ ( x ^ 2 + ( sin 54 ) ^ 2 - 2 * x * ( sin 54 ) ^ 2 ) ) ^ 2 + x ^ 2 - 2 * x * ( x + √ ( x ^ 2 + ( sin 54 ) ^ 2 - 2 * x * ( sin 54 ) ^ 2 ) * cos 72 ) ≥ 0        (4 )

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    From inequality(1)：
         k < -0.127007
    From inequality(2)：
         k ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(3)：
         k ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(4)：
         k ≥ -0.169983

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    From inequalities (1) and (2)
         k < -0.127007    (5)
    From inequalities (3) and (5)
         k < -0.127007    (6)
    From inequalities (4) and (6)
         -0.169983 ≤ k < -0.127007    (7)

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    The final solution set is :
         -0.169983 ≤ k < -0.127007
    *Note: Radian.

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