If a2 + b2 + c2 + 216 = 12 ( a + b - 2c) , then 
is :
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 6
a2 + b2 + c2 + 216 = 12(a + b - 2c)
(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 - 2ab
a2 + b2 + c2 + 216 = 12(a + b - 2c)
a2 - 12a + b2 - 12b + c2 + 24c + 216 = 0
a2 - 12a + 36 + b2 - 12b + 36 + c2 + 24c + 144 = 0
(a - 6)2 + (b - 6)2 + (c + 12)2 = 0
a = 6, b = 6, c = -12
√(ab - bc + ca) = √[(6 × 6) - (6 × -12) + (-12 × 6)] = √(36 + 72 - 72) = √36 = 6