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Assignment:Find the solution set of inequality 0 <(4x^2+1)/(x^2-x+1) <3 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
0 < ( 4 * x ^ 2 + 1 ) / ( x ^ 2 - x + 1 ) (1)
( 4 * x ^ 2 + 1 ) / ( x ^ 2 - x + 1 ) <3 (2)
From the definition field of divisor
x ^ 2 - x + 1 ≠ 0 (3 )
From inequality(1):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
-3.561553 < x < 0.561553
From inequality(3):
x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequalities (1) and (2)
-3.561553 < x < 0.561553 (4)
From inequalities (3) and (4)
-3.561553 < x < 0.561553 (5)
The final solution set is :
-3.561553 < x < 0.561553 Your problem has not been solved here? Please take a look at the hot problems !