Question

If pqr=1 then prove:

(1\1+p+q​​​​​^{​​​​​​q-1}) + (1\1+q+r​​​​​^{​​​​​​-1}) +(1\1+p+r^{​​​​​​-1})=1

Answer 1

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