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Assignment:Find the solution set of inequality 100/(1+(x-1)^1.2) <(2.5*(sqrt(2*x+0.25)-0.5))/x .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
100 / ( 1 + ( x - 1 ) ^ 1.2 ) < ( 2.5 * ( sqrt ( 2 * x + 0.25 ) - 0.5 ) ) / x (1)
From the definition field of divisor
1 + ( x - 1 ) ^ 1.2 ≠ 0 (2 )
From the definition field of √
2 * x + 0.25 ≥ 0 (3 )
From the definition field of divisor
x ≠ 0 (4 )
From inequality(1):
x > 125.11639
From inequality(2):
x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequality(3):
x ≥ -1/8
From inequality(4):
x < 0 或 x > 0
From inequalities (1) and (2)
x > 125.11639 (5)
From inequalities (3) and (5)
x > 125.11639 (6)
From inequalities (4) and (6)
x > 125.11639 (7)
The final solution set is :
x > 125.11639Your problem has not been solved here? Please take a look at the hot problems !