If pqr=1, then prove that [ 1/(1+p+q-1)] + [1/(1+q+r-1)] + [1/(1+r+p-1)] = 1 - Maths - Number Systems

Question

If pqr=1, then prove that [ 1/(1+p+q-1)] +
[1/(1+q+r-1)] + [1/(1+r+p-1)] = 1

Sahil Sharma · Accepted Answer

pqr = 1
r = 1/pq
1/r = pq
(1/1+p+q-1) + (1/1+q+r-1) +
(1/1+r+p-1)
(1/(1+p+1/q) + (1/(1+q+pq) + (1/(1+1/pq+1/p)
(1/(q+pq+1/q) + (1/(q+pq+1) + (1/(q+pq+1/pq)
(q/q+pq+1) + (1/q+pq+1) + (pq/q+pq+1)
(q+pq+1) / (q+pq+1)
= 1
hence proved