Question

if a, b, c are in continued proportion prove that
a2+b2/b2+c2 = a/c​

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

Continued proportion means, a/b=b/c