Question
If b is the mean proportion to a and c with a common
ratio∛(2/3) , then (a – b)3 : (b – c)3 is:Solution
b = √ac Then, (a - b)3 ∶ (b - c)3 = (a - √ac)3 ∶ (√ac - c)3 ⇒ [√a(√a - √c)]3 ∶ [√c(√a - √c]3 ⇒ (√a/√c)3 We know that, a × (common ratio)2 = c Or, (√2/√3)2/3 = c/a Then, (√a/√c)3 = [(√3/√2)2/3]3 ⇒ 3 ∶ 2 ∴ The required solution is 3 ∶ 2
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