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[ 1/1Inequality]
Assignment:Find the solution set of inequality 1 <= sqrt(x^2+4*x+9-12*x) <= 3 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
1 <= sqrt ( x ^ 2 + 4 * x + 9 - 12 * x ) (1)
sqrt ( x ^ 2 + 4 * x + 9 - 12 * x ) <= 3 (2)
From the definition field of √
x ^ 2 + 4 * x + 9 - 12 * x ≥ 0 (3 )
From inequality(1):
x ≤ 1.171573 或 x ≥ 6.828427
From inequality(2):
0 ≤ x ≤ 8
From inequality(3):
x ≤ 1.354249 或 x ≥ 6.645751
From inequalities (1) and (2)
0 ≤ x ≤ 1.171573 或 6.828427 ≤ x ≤ 8 (4)
From inequalities (3) and (4)
0 ≤ x ≤ 1.171573 或 6.828427 ≤ x ≤ 8 (5)
The final solution set is :
0 ≤ x ≤ 1.171573 或 6.828427 ≤ x ≤ 8Your problem has not been solved here? Please take a look at the hot problems !