If a, b, c are positive and a + b + c = 1, then the least value of $$\frac{1}{a}$$  + $$\frac{1}{b}$$  + $$\frac{1}{c}$$ is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{For minimum value of}} \cr & \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \cr & a = b = c \cr & a + b + c = 1{\text{ }}\left( {{\text{Given}}} \right) \cr & \therefore a = b = c = \frac{1}{3} \cr & \frac{1}{a} = \frac{1}{b} = \frac{1}{c} = 3 \cr & \therefore {\text{Minimum value of,}} \cr & = \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \cr & = 3 + 3 + 3 \cr & = 9 \cr} $$