<s>[INST] For real $a,b,c$ , if $a^2+b^2+c^2=ab+bc+ac$ ,then the value of $\frac{a+b} {c}$ is? 
For real $a,b,c$ , if $a^2+b^2+c^2=ab+bc+ac$ ,then the value of
  $\frac{a+b} {c}$ is how much?

Ans.
What I could gather:
from the identity,
$$ a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^3-ab+bc+ca)$$
We gather that RHS=0.
$$ =>a^3+b^3+c^3=3abc$$
It would e helpful if someone could tell me how should I proceed.
 [/INST] For $a=b=c=0$ the needed value does not exist.
If $c\neq0$ then since 
$$0=\sum_{cyc}(a^2-ab)=\frac{1}{2}\sum_{cyc}(2a^2-2ab)=\frac{1}{2}\sum_{cyc}(a^2-2ab+b^2)=\frac{1}{2}\sum_{cyc}(a-b)^2,$$
we obtain $a=b=c$ and $\frac{a+b}{c}=2$.
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