If $$a + \frac{1}{b}$$ = $$b + \frac{1}{c}$$ = $$c + \frac{1}{a}$$ $$\left( {a \ne b \ne c} \right)$$ then the value of abc is?
A. $$ \pm {\text{1}}$$
B. $$ \pm {\text{2}}$$
C. 0
D. $$ \pm \frac{1}{2}$$
Answer: Option A
Solution(By Examveda Team)
$$a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a}$$To save your time assume values of a, b, c according to the question.
$$\eqalign{ & {\text{Let }}a = 2,{\text{ }}b = - 1\& c = \frac{1}{2} \cr & 2 + \frac{1}{{ - 1}} = - 1 + \frac{1}{{\frac{1}{2}}} = \frac{1}{2} + \frac{1}{2} \cr & \therefore abc = 2 \times - 1 \times \frac{1}{2} = - 1 \cr} $$
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