Question

If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.

Answer 1

Since a, b, c are in continued proportion,

`a/b = b/c`

`=>` b² = ac

Now, (a² + b²)(b² + c²) = (a² + ac)(ac + c²)

= a(a + c) c(a + c)

= ac(a + c)²

= b²(a + c)²

`=>` (a² + b²)(b² + c²) = [b(a + c)][b(a + c)]

`=> (a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`