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Question

If a+b+c=11 and ab+bc+ac=32
find
a2+b2+c2


A

57

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B

67

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C

89

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D

45

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Solution

The correct option is A

57


Given (a+b+c)=11 and (ab+bc+ca)=32
(a+b+c)2=112
a2+b2+c2+2(ab+bc+ca)=121
a2+b2+c2+2(32)=121
a2+b2+c2+64=121
a2+b2+c2=12164=57


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