Question : If $a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}(a\neq b\neq c)$, then the value of $abc$ is:
Option 1: $\pm 1$
Option 2: $\pm 2$
Option 3: $0$
Option 4: $\pm \frac{1}{2}$
Correct Answer: $\pm 1$
Solution :
$a+\frac{1}{b}=b+\frac{1}{c}$
⇒ $(a-b) = \frac{(b-c)}{bc}$ ----------(i)
$a+\frac{1}{b}=c+\frac{1}{a}$
⇒ $(a-c) = \frac{(b-a)}{ba}$ ----------(ii)
$b+\frac{1}{c}=c+\frac{1}{a}$
⇒ $(b-c) = \frac{(c-a)}{ca}$ -----------(iii)
Multiplying (i), (ii) and (iii),
⇒ $(a-b)(a-c)(b-c) = \frac{(b-c)(b-a)(c-a)}{bc×ba×ca}$
⇒ $1 = \frac{1}{(abc)^2}$
⇒ $abc = \pm 1$
Hence, the correct answer is $\pm 1$.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
