Question

If pqr = 1 then
($$(\frac{1}{1 + p + q^-1}) $+$ $(\frac{1}{1 + q + r^-1})$ $+$ (\frac{1}{1 + r + p^-1})$$) is equal to

• A. 1
• B. pq
• C. qr
• D. $\frac{1}{pq}$

Answer 1

Answer: (A)

1

Answer 2

In the question it is given that $pqr$ = 1

The equation given is $((\frac{1}{1 + p + q^-1})$ + $(\frac{1}{1 + q + r^-1})$ + $(\frac{1}{1 + r + p^-1}))$

= $\frac{1}{1+ q + \frac{1}{q}} + \frac{1}{1+ q + \frac{1}{r}} + \frac{1}{1+ q + \frac{1}{p}}$

= $\frac{q}{1+ q + pq} + \frac{1}{1+ q + pq} + \frac{q}{1+ \frac{1}{pq} + \frac{1}{p}}$

= $\frac{q}{1+ q + pq} + \frac{1}{1+ q + pq} + \frac{pq}{1+ q + pq}$

$\frac{1 + q + pq}{1+ q + pq} = 1$

The correct option is (A): 1