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Assignment:Find the solution set of inequality (√xlnx)/(x-1) <1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( √ x * ln x ) / ( x - 1 ) <1 (1)
From the definition field of √
x ≥ 0 (2 )
From the definition field of ln
x > 0 (3 )
From the definition field of divisor
x - 1 ≠ 0 (4 )
From inequality(1):
x < 1 或 x > 1
From inequality(2):
x ≥ 0
From inequality(3):
x > 0
From inequality(4):
x < 1 或 x > 1
From inequalities (1) and (2)
0 ≤ x < 1 或 x > 1 (5)
From inequalities (3) and (5)
0 < x < 1 或 x > 1 (6)
From inequalities (4) and (6)
0 < x < 1 或 1 < x < 1 或 x > 1 (7)
The final solution set is :
0 < x < 1 或 1 < x < 1 或 x > 1Your problem has not been solved here? Please take a look at the hot problems !