Question

if a b c are in continued proportion prove that
a^2+b^2/b^2+c^2 = a/ c ​

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If a, b, c are in continued proportion, prove that a : c = (a2 + b2) : (b2 + c2)

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asked Feb 22, 2019 in Class X Maths by priya12 (-12,631 points)

If a, b, c are in continued proportion, prove that a : c = (a2 + b2) : (b2 + c2)

ratio and proportion

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answered Feb 22, 2019 by navnit40 (-4,939 points)

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.

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