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the value of (a^2 + b^2 + c^2)

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the value of (a^2 + b^2 + c^2)

by sanju09 » Wed Mar 23, 2011 2:17 am
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




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by manpsingh87 » Wed Mar 23, 2011 2:36 am
sanju09 wrote: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




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a^2 + 2 b = 7 1)
b^2 + 4 c = -7 2)
c^2 + 6 a = -14 3)

adding 1,2,3 we get
a^2+6a+b^2+2b+c^2+4c= -14;

(a^2+6a+9)+(b^2+2b+1)+(c^2+4c+4) - 14 =-14;

(a+3)^2+(b+1)^2+(c+2)^2=0;
now for rhs to become each term on the lhs must become zero i.e. a=-3;b=-1;c=-2;

putting these values in the expression a^2+b^2+c^2 we get 9+1+4 = 14 hence A
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