If a, b, c and d are in continued proportion, prove that ad(c² + d²) = c³(b + d).
Ratio Proportion
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Question

If a, b, c and d are in continued proportion, prove that ad(c2 + d2) = c3(b + d).

KnowledgeBoat · Accepted Answer

Since, a, b, c, d are in continued proportion. (let). c = dk, b = ck = (dk)k = dk2, a = bk = (dk2)k = dk3. Substituting values in L.H.S. of the equation ad(c2 + d2) = c3(b + d), we get : L.H.S = ad(c2 + d2) = dk3.(d).[(dk)2 + d2] = d2k3.[d2(k2 + 1)] = d4k3(k2 + 1). Substituting values in R.H.S. of the equation ad(c2 + d2) = c3(b + d), we get : R.H.S = c3(b + d) = (dk)3.(dk2 + d) = d3k3[d(k2 + 1)] = d4k3(k2 + 1). Since, L.H.S = R.H.S Hence, proved that ad(c2 + d2) = c3(b + d).

Mathematics

If a, b, c and d are in continued proportion, prove that ad(c² + d²) = c³(b + d).

Ratio Proportion

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