Question

If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`

Answer 1

Given, a, b and c are in continued proportion.

Therefore,

`a/b = b/c`

ac = b²

Here,

`(a^2 + ab + b^2)/(b^2 + bc + c^2) = (a^2 + ab + ac)/(ac + bc + c^2)`

= `(a(a + b + c))/(c(a + b + c))`

= `a/c`

Hence proved.