If a^2 + 2 b = 7, b^2 + 4 c = -7 and c^2 + 6 a = -14, then what is the value of (a^2 + b^2 + c^2)?
(A) 14
(B) 25
(C) 36
(D) 47
(E) 49
(A) 14
(B) 25
(C) 36
(D) 47
(E) 49
adding all three eqs ..
a^2 + b^2 +c^2 + 6a +2b +4c = -14
a^2 + b^2 +c^2 = -14 - (6a +2b +4c) [even - even = even]
B, D and E are eliminated.
a^2 + 2 b = 7
odd + even = odd
a = odd
b^2 + 4 c = -7
odd + even = odd
b = odd
c^2 + 6 a = -14
even + even = even
c = even
a^2 + b^2 +c^2 = -14 - (6a +2b +4c)
dividing both sides by 2
(a^2 + b^2 +c^2)/2 = -7 - (3a +b +2c) = odd - (odd+odd-even) = odd
(a^2 + b^2 +c^2)/2 = odd
Only A satisfies.
Option A is the correct answer.
