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Assignment:Find the solution set of inequality sqrt(4x^2-4x+2)-sqrt(x^2+1)-x+1 <0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( 4 * x ^ 2 - 4 * x + 2 ) - sqrt ( x ^ 2 + 1 ) - x + 1 <0 (1)
From the definition field of √
4 * x ^ 2 - 4 * x + 2 ≥ 0 (2 )
From the definition field of √
x ^ 2 + 1 ≥ 0 (3 )
From inequality(1):
x > 1
From inequality(2):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(3):
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 (4)
From inequalities (3) and (4)
x > 1 (5)
The final solution set is :
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