Question

If $a,b$ and $c$ are positive real numbers then $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$ is greater than or equal to.

• A. $3$
• B. $6$
• C. $27$
• D. $5$

Answer 1

The correct option is A $3$

Using $AM\ge GM$
$\frac{\frac{a}{b}+\frac{b}{c}+\frac{c}{a}}{3}\ge {(\frac{a}{b}\times \frac{b}{c}\times \frac{c}{a})}^{1/3}$
$\Rightarrow \frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge 3$
Hence, option 'A' is correct.