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
Explanation
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.
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