Question

If p : q is the sub-duplicate ratio of

Answer 1

Answer:

The sub-duplicate ratio of m:n is ✓m:√n.

It is given that p:q is the sub-duplicate ratio of

p-x² : q-x².

⇒p−x2√q−x2√=pq⇒p−x2q−x2=p2q2.

⇒q2(p−x2)=p2(q−x2)⇒pq2−q2x2=qp2−p2x2.

⇒p2x2−q2x2=qp2−pq2⇒x2(p2−q2)=pq(p−q).

⇒x2=pq(p−q)p2−q2=pqp+q⋯( provided p≠q).