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Assignment:Find the solution set of inequality (-2x+sqrt(4(x)^2-12))^2+x*(-2x+sqrt(4(x)^2-12))+1 <0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( -2 * x + sqrt ( 4 * ( x ) ^ 2 - 12 ) ) ^ 2 + x * ( -2 * x + sqrt ( 4 * ( x ) ^ 2 - 12 ) ) + 1 <0 (1)
From the definition field of √
4 * ( x ) ^ 2 - 12 ≥ 0 (2 )
From the definition field of √
4 * ( x ) ^ 2 - 12 ≥ 0 (3 )
From inequality(1):
x > 2.245366
From inequality(2):
x ≤ -√3 或 x ≥ √3
From inequality(3):
x ≤ -√3 或 x ≥ √3
From inequalities (1) and (2)
x > 2.245366 (4)
From inequalities (3) and (4)
x > 2.245366 (5)
The final solution set is :
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