If a, b, c, d are in continued proportion, prove that :(((a-b)/c) + ((a-c)/b))²

Question

KnowledgeBoat · Accepted Answer

Given a, b, c, d are in continued proportion. ∴ a : b = b : c = c : d = k (let) ⇒ c = dk, b = ck = (dk)k = dk2, a = bk = (dk2)k = dk3. Substituting values of a, b and c in L.H.S. of , we get : Substituting values of a, b and c in R.H.S. of , we get : Since, L.H.S. = R.H.S. Hence, proved that .

Mathematics

If a, b, c, d are in continued proportion, prove that :(((a-b)/c) + ((a-c)/b))²

Ratio Proportion

Related Questions

If a, b, c, d are in continued proportion, prove that :
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Mathematics

If a, b, c, d are in continued proportion, prove that :(((a-b)/c) + ((a-c)/b))²

Ratio Proportion

Related Questions

If a, b, c, d are in continued proportion, prove that :(a + b)(b + c) - (a + c)(b + d) = (b - c)2

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If a, b, c, d are in continued proportion, prove that :
(a + b)(b + c) - (a + c)(b + d) = (b - c)²

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(a² − b²)(c² − d²) = (b² − c²)²