Question

${\left(\frac{p}{q}\right)}^{\left(a\right)}\times {\left(\frac{q}{r}\right)}^{\left(b\right)}\times {\left(\frac{r}{p}\right)}^{\left(c\right)}=1.Whatistherelationshipbetweena,b,c?$

• A. a=b=c
• B. abc=0
• C. a+b+c = 0
• D. abc = 1/2
• E. None of these

Answer 1

The correct option is A

a=b=c

${\left(\frac{p}{q}\right)}^a\times {\left(\frac{q}{r}\right)}^b\times {\left(\frac{r}{p}\right)}^c=p^o\times q^o\times r^o$


$p^{a-c}\times q^{b-a}\times r^{c-b}=p^o\times q^o\times r^o$

$So,a-c=0$

$b-a=0$

$c-b=0$


$Hence,a=b=c$