If $$a + \frac{1}{b}$$ = $$b + \frac{1}{c}$$ = $$c + \frac{1}{a}$$ (where a ≠ b ≠ c), then abc is equal to?
A. +1
B. -1
C. +1 & -1
D. None of these
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a} \cr & {\text{Put , }}a = \frac{1}{2},b = 2,c = - 1 \cr & \Rightarrow \frac{1}{2} + \frac{1}{2} = 2 - 1 = - 1 + 2 \cr & \Rightarrow 1 = 1 = 1 \cr & abc = \frac{1}{2} \times 2 \times - 1 \cr & \boxed{abc = - 1} \cr & {\text{Again put}} \cr & a = - \frac{1}{2},b = - 2,c = 1 \cr & \Rightarrow a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a} \cr & \Rightarrow - \frac{1}{2} - \frac{1}{2} = - 2 + 1 = 1 - 2 \cr & \Rightarrow - 1 = - 1 = - 1 \cr & {\text{Equation satisfied}} \cr & \Rightarrow abc = - \frac{1}{2} \times - 2 \times 1 \cr & \boxed{abc = + 1} \cr & {\text{So, }}abc{\text{ can be }} - 1{\text{ and }} + 1 \cr} $$Join The Discussion
Comments ( 1 )
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anyone can explain it please how we can put the value of a, b, and c without finding?