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Assignment:Find the solution set of inequality sqrt(r^2+200r+10000-400)-sqrt(r^2-200r+10000-400) >200 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( r ^ 2 + 200 * r + 10000 - 400 ) - sqrt ( r ^ 2 - 200 * r + 10000 - 400 ) >200 (1)
From the definition field of √
x ^ 2 + 200 * x + 10000 - 400 ≥ 0 (2 )
From the definition field of √
x ^ 2 - 200 * x + 10000 - 400 ≥ 0 (3 )
From inequality(1):
The solution set is empty, that is, within the range of real numbers, the inequality will never be established!
From inequality(2):
r ≤ -120 或 r ≥ -80
From inequality(3):
r ≤ 80 或 r ≥ 120
The final solution set is :
The solution set is empty,that is, the inequality will never be estatlished within the real number range.
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