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☆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 :
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