Question

pls solve above question.
its urgent​

Answer 1

Answer:

     (x² + y²)/(p² + q²)  =  xy / pq

⇒  (x² + y²)pq = (p² + q²)xy         ...(1)

⇒  (x² + y²)pq - 2xypq = (p² + q²)xy - 2xypq

⇒  (x² + y² - 2xy)pq  =  (p² + q² - 2pq)xy

⇒  (x - y)²pq  =  (p - q)²xy

⇒  (x - y)² / (p - q)²  =  xy / pq         ...(2)

Also from (1),

⇒  (x² + y²)pq + 2xypq = (p² + q²)xy + 2xypq

⇒  (x² + y² + 2xy)pq  =  (p² + q² + 2pq)xy

⇒  (x + y)²pq  =  (p + q)²xy

⇒  (x + y)² / (p + q)²  =  xy / pq         ...(3)

Equations (2) and (3) give

    (x + y)² / (p + q)²  =  (x - y)² / (p - q)²

⇒  (x + y)² / (x - y)²  =  (p + q)² / (p - q)²

⇒  (x + y) / (x - y)  =  (p + q) / (p - q)

(Well, really the last line should have a "±" in it, but we may as well suppose that x>y and p>q so both sides have the same sign).