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Assignment:Find the solution set of inequality sqrt(k/2)-sqrt(2*k+1)/2 <0.15/sqrt(0.6) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( k / 2 ) - sqrt ( 2 * k + 1 ) / 2 <0.15 / sqrt ( 0.6 ) (1)
From the definition field of √
x / 2 ≥ 0 (2 )
From the definition field of √
2 * x + 1 ≥ 0 (3 )
From inequality(1):
k ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
k ≥ 0
From inequality(3):
k ≥ -1/2
From inequalities (1) and (2)
k ≥ 0 (4)
From inequalities (3) and (4)
k ≥ 0 (5)
The final solution set is :
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