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Question

a2 + b2 + c2 - ab - bc - ca equals:


A

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B

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C

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Solution

The correct option is C


a2 + b2 + c2 - ab - bc - ca

= 1/2(2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca)

= 1/2(a2 - 2ab + b2 + b2 - 2bc + c2 + c2 - 2ca + a2)

= 1/2[(a - b)2 + (b - c)2 + (c - a)2]


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