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Let a and b be positive real numbers such that a + b = 1. Find set of all possible values of 1/a + 1/b.

 Mar 25, 2020
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Let a and b be positive real numbers such that a + b = 1. Find set of all possible values of 1/a + 1/b.

 

Hello Guest!

 

\(a+b=1\\ a=1-b\\ \frac{1}{a}+\frac{1}{b}= \frac{1}{1-b}+\frac{1}{b}=\frac{b+1-b}{b-b^2}=\frac{1}{b-b^2}\\ \)

 

The set of all possible values of   \(\frac{1}{a}+\frac{1}{b}\)  are \(\{\mathbb R>1\}\ |\ \{a,b\} \subset \mathbb R\ \)und 1> a,b > 0

laugh  !

 Mar 25, 2020
edited by asinus  Mar 25, 2020
edited by asinus  Mar 25, 2020
edited by asinus  Mar 25, 2020
edited by asinus  Mar 25, 2020

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