Question

if a,b,c,d are in proportion prove that a²+b²/c²+d²=ab+ad-bc/bc+cd-ad​

Answer 1

Answer:

If a, b, c, d, are in continued proportion, prove that (a+b)(b+c) -(a+c)(b+d=(b-c)^2

a2 + c2), (ab + cd) and (b2 + d2) are in continued proportion.

⇒ (a2 + c2) : (ab + cd) = (ab + cd) : (b2 + d2)

⇒ (a2 + c2) (b2 + d2) = (ab + cd) (ab + cd)

⇒ a2b2 + a2d2 + c2b2 + c2d2 = a2b2 + 2abcd + c2d2

⇒ a2d2 + c2b2 – 2abcd = 0

⇒ (ad – cb)2 = 0

⇒ ad – cb = 0

⇒ ad = bc

⇒ a/b = c/d

⇒ a, b, c and d are in proportion.

Step-by-step explanation:

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Answer 2

Answer:

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