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If a, b, c, d, e are in continued proportion, prove that a^2+b^2+c^2+d^2,ab+bc+cd+de,b^2+c^2+d^2+e^2 |
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Answer» (i) Since a, B, c, d are in continued proportion then a/b = b/c = c/d = k ⇒ a = bk, b = ck , c = dk ⇒ a = ck2 ⇒ a = dk3, b = dk2 and c = dk (ii) L.H.S. = (d2k6 + d2k4 + d2k2)(d2k4 + d2k2 + d2) = d2k2 (K4 + k2 + 1).d2 (k4 + k2 + 1) = d4k2(k4 + k2 + 1)2 R.H.S. = (ab + bc + cd)2 = (dk3.dk2 + dk2.dk + dk.d)2 = d4.k2(k4 + k2 + 1)2 L.H.S. = R.H.S. Hence proved. |
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