Question

Using a^ 2 +b^ 2 +c^ 2 -ab-bc-ca= 1 2 \ (a-b)^ 2 +(b-c)^ 2 +(c-a)^ 2 \ . Prove that if a ^ 2 + b ^ 2 + c ^ 2 = ab + bc + ca then a = b = c​

Answer 1

Answer:

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Answer 2

Answer:

bc−a2ca−b2ab−c2ca−b2ab−c2bc−a2ab−c2bc−a2ca−b2∣∣∣∣∣∣∣∣

This matrix is cofactor matrix of ∣∣∣∣∣∣∣∣abcbcacab∣∣∣∣∣∣∣∣

Thus, by property of cofactor matrix,

∣∣∣∣∣∣∣∣bc−a2ca−b2ab−c2ca−b2ab−c2bc−a2ab−