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Assignment:Find the solution set of inequality {-1/m+[1/(m^2)-2/m+6]^(1/2)}^2-8 >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( -1 / m + ( 1 / ( m ^ 2 ) - 2 / m + 6 ) ^ ( 1 / 2 ) ) ^ 2 - 8 >0 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of divisor
x ^ 2 ≠ 0 (3 )
From the definition field of divisor
x ≠ 0 (4 )
From inequality(1):
m ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
m < 0 或 m > 0
From inequality(3):
m < 0 或 m > 0
From inequality(4):
m < 0 或 m > 0
From inequalities (1) and (2)
m < 0 或 m > 0 (5)
From inequalities (3) and (5)
m < 0 或 0 < m < 0 或 m > 0 (6)
From inequalities (4) and (6)
m < 0 或 0 < m < 0 或 m > 0 (7)
The final solution set is :
m < 0 或 0 < m < 0 或 m > 0Your problem has not been solved here? Please take a look at the hot problems !