prove that a^2+b^2+c^2-ab-bc-ca is always non negative for all the value of a' b and c

Answer 1

(a-b)^2 + (a-c)^2 + (b-c)^2 >= 0

a^2 - 2ab + b^2 + a^2 - 2ac + c^2 + b^2 - 2bc + c^2 >= 0

2a^2 + 2b^2 + 2c^2 - 2(ab+ac+bc) >= 0

divide by 2.