Question

if r^2=pq show that p:q is the duplicate ratio of (p+r):(q+r)

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

Given : r² = pq

Now,

duplicate ratio of (p+r) : (q +r)

= (p+r)² : (q+r)²

= (p² + r² + 2pr) : (q² + r² + 2qr)

= (p² + pq + 2pr) : (q² + pq + 2qr)

= p(p + q + 2r) : q(q + p + 2r)

= p : q

Thus, p:q is the duplicate ratio of (p+r) : (q+r).

(SEE THE ATTACHMENT TOO)

♧♧HOPE THIS HELPS YOU♧♧