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Assignment:Find the solution set of inequality sqrt(2x-3)+sqrt(3x-5) >sqrt(5x-6) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( 2 * x - 3 ) + sqrt ( 3 * x - 5 ) > sqrt ( 5 * x - 6 ) (1)
From the definition field of √
2 * x - 3 ≥ 0 (2 )
From the definition field of √
3 * x - 5 ≥ 0 (3 )
From the definition field of √
5 * x - 6 ≥ 0 (4 )
From inequality(1):
x > 2
From inequality(2):
x ≥ 3/2
From inequality(3):
x ≥ 5/3
From inequality(4):
x ≥ 6/5
From inequalities (1) and (2)
x > 2 (5)
From inequalities (3) and (5)
x > 2 (6)
From inequalities (4) and (6)
x > 2 (7)
The final solution set is :
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