Let \(a\) and \(b\) be positive real numbers such that \(a + b = 1.\) Find set of all possible values of \(\frac{1}{a} + \frac{1}{b}.\)
\(b=1-a\\ \dfrac 1 a + \dfrac 1 b = \\ \dfrac 1 a + \dfrac{1}{1-a} = \\ \dfrac{1-a+a}{a(1-a)} = \\ \dfrac{1}{a(1-a)} \in (-\infty,0) \cup [4,\infty)\)
The sum has to be positive
duh, right you are.
it's just \([4, \infty)\)
It is good to see that our answers are getting looked at
Thanks Rom and guest.
+170 
