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Question

If a+b+c=12 and a2+b2+c2=50, then ab + bc + ca = .

A
84
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B
88
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C
47
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D
94
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Solution

The correct option is C 47
It is given that a+b+c=12

Using identity ,
(a+b+c)2=a2+b2+c2+2 (ab+ac+bc), we have

122=a2+b2+c2+2 (ab+ac+bc)

Substituting the value of a2+b2+c2 which is 50,we get
144=50+2 (ab+ac+bc)
2 (ab+ac+bc)=14450
2 (ab+ac+bc)=94
ab+ac+bc=47

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