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Question

# If a2+2b=7,b2+4c=âˆ’7 and c2+6a=âˆ’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 14Given a2+2a=7,b2+4c=−7 and c2+6a=−14Then, a2=7−2b ,b2=−7−4c, c2=−14−6aAdd three equation thena2=7−2b ,b2=−7−4c , c2=−14−6a⇒a2+b2+c2+6a+2b+4c+14=0⇒a2+6a+9+b2+2b+1+c2+4c+4=0⇒(a+3)2+(b+1)2+(c+2)2=0 Hence (a+3)2=0⇒a+3=0⇒a=−3Or (b+1)2=0⇒b+1=0 and b=−1Also (c+2)2=0⇒c+2=0⇒c=−2Then, a2+b2+c2=(−3)2+(−1)2+(−2)2=9+1+4=14

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