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Assignment:Find the solution set of inequality lg(xx-4x-21)+sqrtx-sqrtx <2 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
lg ( x * x - 4 * x - 21 ) + sqrt x - sqrt x <2 (1)
From the definition field of lg
x * x - 4 * x - 21 > 0 (2 )
From the definition field of √
x ≥ 0 (3 )
From the definition field of √
x ≥ 0 (4 )
From inequality(1):
x < 13.18034
From inequality(2):
x < -3 或 x > 7
From inequality(3):
x ≥ 0
From inequality(4):
x ≥ 0
From inequalities (1) and (2)
x < -3 或 7 < x < 13.18034 (5)
From inequalities (3) and (5)
7 < x < 13.18034 (6)
From inequalities (4) and (6)
7 < x < 13.18034 (7)
The final solution set is :
7 < x < 13.18034 Your problem has not been solved here? Please take a look at the hot problems !