If ab + bc + ca = 8 and a2 + b2 + c2 = 20, then a possible value of 1/2 (a + b + c)[(a - b)2 + (b - c)2 + (c - a)2] is:

Answer: Option A

ab + bc + ca = 8
a² + b² + c² = 20
a² + b² + c² - ab - bc - ca = $$\frac{1}{2}$$[(a - b)² + (b - c)² + (c - a)²]
20 - 8 = $$\frac{1}{2}$$[(a - b)² + (b - c)² + (c - a)²)]
12 = $$\frac{1}{2}$$[(a - b)² + (b - c)² + (c - a)²]
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
a + b + c = $$\sqrt{20+2\times 8}=6$$
$$\frac{1}{2}$$(a + b + c)[(a - b)² + (b - c)² + (c - a)²]
= 12(a + b+ c)
= 12 × 6
= 72