If x = a (b - c), y = b (c - a), z = c (a - b), then the value of ( x/a )^3 + ( y/b )^3 + ( z/c )^3 is :

Answer: Option D

Given x = a (b - c), y = b (c - a), z = c (a - b)
x = a (b - c)
⇒ $$\frac{x}{a}$$ = b - c ..... (i)
Similarly, y = b (c - a)
⇒ $$\frac{y}{b}$$ = c - a ..... (ii)
And similarly z = c (a - b)
⇒ $$\frac{z}{c}$$ = c - a ..... (iii)
Adding (i), (ii) and (iii) we get
∵ $$\frac{x}{a}$$ + $$\frac{y}{b}$$ + $$\frac{z}{c}$$ = b - c + c - a + a - b
⇒ $$\frac{x}{a}$$ + $$\frac{y}{b}$$ + $$\frac{z}{c}$$ = 0
$$\begin{array}{rl}& \therefore {\left(\frac{x}{a}\right)}^3+{\left(\frac{y}{b}\right)}^3+{\left(\frac{z}{c}\right)}^3\\ & =3\times \frac{x}{a}\times \frac{y}{b}\times \frac{z}{c}\\ & =\frac{3xyz}{abc}\end{array}$$
[If a + b + c = 0, a³ + b³ + c³ = 3abc]