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☆1 inequalities
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Assignment:Find the solution set of inequality sqrt(4a^2*(1+2/a))/a ≥1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( 4 * a ^ 2 * ( 1 + 2 / a ) ) / a ≥1 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of √
4 * x ^ 2 * ( 1 + 2 / x ) ≥ 0 (3 )
From the definition field of divisor
x ≠ 0 (4 )
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
From inequality(3):
a ≤ -2 或 a ≥ 0
From inequality(4):
a < 0 或 a > 0
From inequalities (1) and (2)
a < 0 或 a > 0 (5)
From inequalities (3) and (5)
a ≤ -2 或 a > 0 (6)
From inequalities (4) and (6)
a ≤ -2 或 a > 0 (7)
The final solution set is :
a ≤ -2 或 a > 0Your problem has not been solved here? Please take a look at the hot problems !