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Let a and b be positive real numbers

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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

!

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