Question

If a, b, c, d are in proportion, then prove that a^2+ab+b^2/a^2−ab+b^2= c^2+cd+d^2/c^2−cd+d^2

Answer 1

Answer:

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Step-by-step explanation:

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.