Question

if P:Q is the sub duplicate ratio of P - x2 : q- x2 then
x2 is

Answer 1

Answer:

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

It is given that p:qp:q is the sub-duplicate ratio of p−x2:q−x2.p−x2:q−x2.

⇒p−x2√q−x2√=pq⇒p−x2q−x2=p2q2.⇒p−x2q−x2=pq⇒p−x2q−x2=p2q2.

⇒q2(p−x2)=p2(q−x2)⇒pq2−q2x2=qp2−p2x2.⇒q2(p−x2)=p2(q−x2)⇒pq2−q2x2=qp2−p2x2.

⇒p2x2−q2x2=qp2−pq2⇒x2(p2−q2)=pq(p−q).⇒p2x2−q2x2=qp2−pq2⇒x2(p2−q2)=pq(p−q).

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