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Assignment:Find the solution set of inequality 6 ≤sqrt(100+xx)-x <8 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
6 ≤ sqrt ( 100 + x * x ) - x (1)
sqrt ( 100 + x * x ) - x <8 (2)
From the definition field of √
100 + x * x ≥ 0 (3 )
From inequality(1):
x ≤ 16/3
From inequality(2):
x > 9/4
From inequality(3):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequalities (1) and (2)
9/4 < x ≤ 16/3 (4)
From inequalities (3) and (4)
9/4 < x ≤ 16/3 (5)
The final solution set is :
9/4 < x ≤ 16/3 Your problem has not been solved here? Please take a look at the hot problems !