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

The Correct Option is A

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