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