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Question
Find the mean proportional between a – b and a3 – a2b
Solution
Let the mean proportional between a – b and a3 – a2b be x.
`\implies` a – b, x, a3 – a2b are in continued proportion.
`\implies` a – b : x = x : a3 – a2b
`\implies` x × x = (a – b)(a3 – a2b)
`\implies` x2 = (a – b) a2(a – b) = [a(a – b)]2
`\implies` x = a(a – b)
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