Question

) If a, b, c are in continued proportion, then show that (a+b2b+c​

Answer 1

Answer:

a, b and c are the continued proportion

 a : b = b : c

⇒ a/b = b/c

⇒ b2 = ac

Now   a/c = a2 + b2/b2 + c2

⇒  a(b2 + c2) = c(a2 + b2)

L.H.S. = a(b2 + c2) ⇒ a(ac + c2) ⇒ ac(a + c)

R.H.S. = c(a2 + b2) ⇒ c(a2 + ac) ⇒ ac(a + c)

L.H.S. = R.H.S.   Hence  proved.