The value of ((a-b)^3+(b-c)^3+(c-a)^3)/((a-b)(a-c)(c-a))is :

Question

The value of \(\frac{(a-b)^3+(b-c)^3+(c-a)^3}{(a-b)(b-c)(c-a)} \) is :

(a) 1 

(b) 3 

(c) 1/3 

(d) Zero

Answer 1

(b) 3

Since a + b + c = 0 ⇒ a³ + b³ + c³ = 3abc. 

So, as (a – b) + (b – c) + (c – a) = 0 

⇒ (a – b)³ + (b – c)³ + (c – a)³ = 3(a – b) (b – c) (c – a)

∴ Given expression = \(\frac{3(a-b)(b-c)(c-a)}{(a-b)(b-c)(c-a)}\) = 3.