If $$a + \frac{1}{b}$$  = $$b + \frac{1}{c}$$  = $$c + \frac{1}{a}$$  (where a ≠ b ≠ c), then abc is equal to?

Solution (By Examveda Team)

$$\eqalign{ & a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a} \cr & {\text{Put , }}a = \frac{1}{2},b = 2,c = - 1 \cr & \Rightarrow \frac{1}{2} + \frac{1}{2} = 2 - 1 = - 1 + 2 \cr & \Rightarrow 1 = 1 = 1 \cr & abc = \frac{1}{2} \times 2 \times - 1 \cr & \boxed{abc = - 1} \cr & {\text{Again put}} \cr & a = - \frac{1}{2},b = - 2,c = 1 \cr & \Rightarrow a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a} \cr & \Rightarrow - \frac{1}{2} - \frac{1}{2} = - 2 + 1 = 1 - 2 \cr & \Rightarrow - 1 = - 1 = - 1 \cr & {\text{Equation satisfied}} \cr & \Rightarrow abc = - \frac{1}{2} \times - 2 \times 1 \cr & \boxed{abc = + 1} \cr & {\text{So, }}abc{\text{ can be }} - 1{\text{ and }} + 1 \cr} $$