Question

Find the mean proportional between a – b and a³ – a²b

Answer 1

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)