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anonymous
 5 years ago
The sum of two positive integers is 9. What is the least possible sum of their reciprocals? Express your answer as a decimal to the nearest hundredth? show all work.
anonymous
 5 years ago
The sum of two positive integers is 9. What is the least possible sum of their reciprocals? Express your answer as a decimal to the nearest hundredth? show all work.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[ A + B = 9 \text {, for } A > 0 \text { and } B > 0 \] \[ \rightarrow A = 9B \] The sum of their reciprocals is \[ S = \frac{1}{A} + \frac{1}{B} = \frac{1}{9B} + \frac{1}{B}\] Find the minimum value for S.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you know calculus?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[ S = \frac{1}{9B} + \frac{1}{B} \] \[ = \frac{B}{B(9B)} + \frac{(9B)}{B(9B)} \] \[ = \frac{9}{B(9B)} = \frac{9}{9B  B^2}\] Now, since the numerator is constant the fraction will be at its smallest value when the denominator is at the largest value. So what is the largest possible value for \[B^2 + 9B + 0\] With B restricted to being > 0.
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