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# Let and be positive real numbers such that Find set of all possible values of ​

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

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Aug 4, 2019
#2
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The sum has to be positive

Guest Aug 4, 2019
#3
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duh, right you are.

it's just $$[4, \infty)$$

Rom  Aug 4, 2019
#4
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It is good to see that our answers are getting looked at

Thanks Rom and guest.

Aug 5, 2019