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If a, b, c are in continued proportion prove that a2+b2/b2+c2 = a/c |
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Answer» d c are the continued proportion a : B = b : c⇒ a/b = b/c⇒ b2 = acNow 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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