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Let \(a\) and \(b\) be positive real numbers such that \(a + b = 1.\) Find set of all possible values of \(\frac{1}{a} + \frac{1}{b}.\)

 Aug 4, 2019
 #1
avatar+6192 
+1

\(b=1-a\\ \dfrac 1 a + \dfrac 1 b = \\ \dfrac 1 a + \dfrac{1}{1-a} = \\ \dfrac{1-a+a}{a(1-a)} = \\ \dfrac{1}{a(1-a)} \in (-\infty,0) \cup [4,\infty)\)

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 Aug 4, 2019
 #2
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+1

The sum has to be positive

Guest Aug 4, 2019
 #3
avatar+6192 
+1

duh, right you are.

 

it's just \([4, \infty)\)

Rom  Aug 4, 2019
 #4
avatar+109763 
0

It is good to see that our answers are getting looked at   laugh

 

Thanks Rom and guest.

 Aug 5, 2019

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