Question

) If pq r = 1, then prove that,
1/(1+p+1/q) + 1/ (1+q+ 1/ r) + 1/ (1+ r+ 1/p) = 1​

Answer 1

1 / ( 1 + p + q^-1) + 1 / ( 1 + q + r^−1) + 1 / (1 + r + p^−1)

= 1 / ( 1 + p + q^−1) + q^−1 / {1+ (q^−1) (r^−1) + q^−1}

+ p / (p + pr + 1)

= 1 / (1 + p + q^−1) + q^−1 / (1 +p + q^−1) + p / (1 + p + q^−1)

(∴pqr=1⇒(qr) ^−1 =p⇒(q^−1) (r^−1) =p and pr=q^−1)

= ( 1 + q^−1 + p ) / (1+ p + q^−1)

= 1