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Assignment:Find the solution set of inequality sqrt(a)+4√a >sqrt(a^2-6)+4√(a^2-6) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( a ) + 4 * √ a > sqrt ( a ^ 2 - 6 ) + 4 * √ ( a ^ 2 - 6 ) (1)
From the definition field of √
x ≥ 0 (2 )
From the definition field of √
x ≥ 0 (3 )
From the definition field of √
x ^ 2 - 6 ≥ 0 (4 )
From the definition field of √
x ^ 2 - 6 ≥ 0 (5 )
From inequality(1):
a < 3
From inequality(2):
a ≥ 0
From inequality(3):
a ≥ 0
From inequality(4):
a ≤ -√6 或 a ≥ √6
From inequality(5):
a ≤ -√6 或 a ≥ √6
From inequalities (1) and (2)
0 ≤ a < 3 (6)
From inequalities (3) and (6)
0 ≤ a < 3 (7)
From inequalities (4) and (7)
√6 ≤ a < 3 (8)
From inequalities (5) and (8)
√6 ≤ a < 3 (9)
The final solution set is :
√6 ≤ a < 3Your problem has not been solved here? Please take a look at the hot problems !