If $$\frac{{{a^2} + {b^2} + {c^2} - 1024}}{{ab - bc - ca}} = - 2$$     and a + b = 5c, where c > 0, then the value of c is . . . . . . . .

A. 8

B. 4

C. 12

D. 5

Answer: Option A

Solution(By Examveda Team)

a + b = 5c
$$\frac{{{a^2} + {b^2} + {c^2} - 1024}}{{ab - bc - ca}} = - 2$$
a² + b² + c² + 2ab - 2bc - 2ac = 1024
(a + b)² + c(c - 2b - 2a) = 1024
(5c)² + c[c - 2(b + a)] = 1024
25c² + c[c - 2 × 5c) = 1024
25c² - 9c² = 1024
16c² = 1024
c² = 64
c = 8