Question

Plzzz help fast plzzz meh apka paw parta hu plzzz kal test hai

Answer 1

Hello

we know,
a2 : b2 is the duplicate ratio of a: b
Now a/c to the question,
p
(p - x) : (q - x) is the duplicate ratio of p : q
So, from the above rule
(p - x) : (q - x)= p2 : q2
(p - x) / (q - x)=p2 /q2
q2(p-x) =p2(q-x)
q2p - q2x = p2q - p2x
q2p - p2q=q2x - p2x
pq(q - p) = (q -p) (q+p)x
pq = (q+p)x
1/x= (q+p)/pq
1/x=1/p + 1/q.
Hence proved.

Hope it helps.