Question

p:q is the sub duplicate ratio of (p-x^2):(q-x^2) . Then x^2 is

A . p/(p+q)
B . q/(p+q)
C . pq/(p+q)
D . None of the above
Please answer I tried but I didn't got answer

Answer 1

I actually had to look this up, had never heard of it.
Subduplicate ratio: The sub duplicate ratio m : n is the ratio √m : √n. So, the sub duplicate ratio of the ratio m22 : n22 is the ratio m : n.

For example:

The sub duplicate ratio of 25 : 81 = √25 : √81 = 5 : 9

so let's just go by that definition:
given:
the sub duplicate ratio of (p-x^2):(q-x^2) = p:q
then
the sub duplicate ratio of √(p-x^2):√(q-x^2) = p:q
square both sides:
(p-x^2)/(q-x^2) = p^2/q^2
pq^2 - q^2 x = qp^2 - p^2x
p^2x - q^2x = qp^2 - pq^2
x(p^2 - q^2) = pq(p - q)
x = pq(p - q)( (p+q)(p-q) )
= pq/(p+q) , where p ≠ q

looks like C