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Assignment:Find the solution set of inequality sqrt(x-1)-sqrt(2x-1) >= sqrt(3x-2) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( x - 1 ) - sqrt ( 2 * x - 1 ) >= sqrt ( 3 * x - 2 ) (1)
From the definition field of √
x - 1 ≥ 0 (2 )
From the definition field of √
2 * x - 1 ≥ 0 (3 )
From the definition field of √
3 * x - 2 ≥ 0 (4 )
From inequality(1):
The solution set is empty, that is, within the range of real numbers, the inequality will never be established!
From inequality(2):
x ≥ 1
From inequality(3):
x ≥ 1/2
From inequality(4):
x ≥ 2/3
The final solution set is :
The solution set is empty,that is, the inequality will never be estatlished within the real number range.
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