Mathematics
语言:中文
Language:English

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 √(x-√(x-√(x-√(x-1)))) <10000 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         √ ( x - √ ( x - √ ( x - √ ( x - 1 ) ) ) ) <10000         (1)
        From the definition field of √
         x - 1 ≥ 0        (2 )
        From the definition field of √
         x - √ ( x - 1 ) ≥ 0        (3 )
        From the definition field of √
         x - √ ( x - √ ( x - 1 ) ) ≥ 0        (4 )
        From the definition field of √
         x - √ ( x - √ ( x - √ ( x - 1 ) ) ) ≥ 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 ≥ 1
    From inequality(3):
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(4):
         x ≥ 1
    From inequality(5):
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!

    From inequalities (1) and (2)
         x ≥ 1    (6)
    From inequalities (3) and (6)
         x ≥ 1    (7)
    From inequalities (4) and (7)
         x ≥ 1    (8)
    From inequalities (5) and (8)
         x ≥ 1    (9)

    The final solution set is :

         x ≥ 1




Your problem has not been solved here? Please take a look at the  hot problems !


Return