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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality (2n+3)/(4n^2-3) ≤1/n .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( 2 * n + 3 ) / ( 4 * n ^ 2 - 3 ) ≤1 / n (1)
From the definition field of divisor
4 * x ^ 2 - 3 ≠ 0 (2 )
From the definition field of divisor
x ≠ 0 (3 )
From inequality(1):
-0.866025 ≤ n ≤ -0.686141 或 0 ≤ n ≤ 0.866025 或 n ≥ 2.186141
From inequality(2):
n < -√3/2 或 -√3/2 < n < √3/2 或 n > √3/2
From inequality(3):
n < 0 或 n > 0
From inequalities (1) and (2)
-√3/2 < n ≤ -0.686141 或 0 ≤ n < √3/2 或 n ≥ 2.186141 (4)
From inequalities (3) and (4)
-√3/2 < n ≤ -0.686141 或 0 < n < √3/2 或 n ≥ 2.186141 (5)
The final solution set is :
-√3/2 < n ≤ -0.686141 或 0 < n < √3/2 或 n ≥ 2.186141Your problem has not been solved here? Please take a look at the hot problems !