a³ - b³ , a² - b² , a² + ab + b² and x are in a proportion. The value of x is ___?

a - b

a + b

b + a

None of these

Given the proportion:

a³ - b³ : a² - b² :: a² + ab + b² : x

We know a³ - b³ = (a - b)(a² + ab + b²) and a² - b² = (a - b)(a + b)

So, the proportion becomes:

(a - b)(a² + ab + b²) : (a - b)(a + b) :: a² + ab + b² : x

Canceling (a - b):

(a² + ab + b²) : (a + b) :: a² + ab + b² : x

This implies x = a + b.