Hard Intermediate Algebra Problem

Question

+1

32

1

+86

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

eramsby1010 May 13, 2024

MaxWong · Answer 1 · 2024-05-13T07:32:26

$\dfrac1{a} + \dfrac1b = \dfrac{a + b}{ab} = \dfrac1{ab}$

Since a and b are positive real numbers, $ab > 0$ . Consequently, $\dfrac1{ab} > 0$ .

Then, $\dfrac1a + \dfrac1b \in (0, \infty)$ .