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Question

If a2+2b=7,b2+4c=7 and c2+6a=14, then the value of (a2+b2+c2) is

A
14
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B
25
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C
36
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D
47
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Solution

The correct option is A 14
Given a2+2a=7,b2+4c=7 and c2+6a=14
Then, a2=72b ,b2=74c, c2=146a
Add three equation then
a2=72b ,b2=74c , c2=146a
a2+b2+c2+6a+2b+4c+14=0a2+6a+9+b2+2b+1+c2+4c+4=0
(a+3)2+(b+1)2+(c+2)2=0
Hence (a+3)2=0a+3=0a=3
Or (b+1)2=0

b+1=0 and b=1

Also (c+2)2=0c+2=0c=2
Then, a2+b2+c2
=(3)2+(1)2+(2)2=9+1+4=14

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