Question

abcd are in continued proportion prove- (a^2-b^2)(c^2-d^2)= (b^2-c^2)^2

Answer 1

Answer:

a, b, c, d in continued proportion

=> a/b = b/c = c/d

=> b²=ac,  c²=bd,  ad = bc   ...   we use these freely!

Then...

( a² - b² ) ( c² - d² )

= ( a² - ac ) ( bd - d² )

= ad ( a - c ) ( b - d )

= bc ( a - c ) ( b - d )

= ( ac - c² ) ( b² - bd )

= ( b² - c² ) ( b² - c² )

= ( b² - c² )²

Answer 2

a/b = b/c = c/d = k(let)

a=bk

a=(dk^2)k

a=dk^3

b=ck

b= (dk)k

b= dk^2

c=dk