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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality (-3a-sqrt((3a)^2-4*(-2a)*(a-2)))/(2*(-2a)) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( -3 * a - sqrt ( ( 3 * a ) ^ 2 - 4 * ( -2 * a ) * ( a - 2 ) ) ) / ( 2 * ( -2 * a ) ) >0 (1)
From the definition field of √
( 3 * x ) ^ 2 - 4 * ( -2 * x ) * ( x - 2 ) ≥ 0 (2 )
From the definition field of divisor
2 * ( -2 * x ) ≠ 0 (3 )
From inequality(1):
a ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
a ≤ 0 或 a ≥ 0.941176
From inequality(3):
a < 0 或 a > 0
From inequalities (1) and (2)
a ≤ 0 或 a ≥ 0.941176 (4)
From inequalities (3) and (4)
a < 0 或 a ≥ 0.941176 (5)
The final solution set is :
a < 0 或 a ≥ 0.941176Your problem has not been solved here? Please take a look at the hot problems !