<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] Write the relation as an equation in $c$
$$c^2 - (a + b) c + a^2 + b^2 - a b = 0$$
The discriminant is $\Delta = (a+b)^2-4(a^2 + b^2 - a b)=-3 (a - b)^2$
It is given that $c\in\mathbb{R}$ thus $\Delta$ must not be negative and the only way is to set $a=b$ and $c=\dfrac{a+b}{2}$
I like this approach not because it is mine, but because is understandable by the average student. 
It's not tricky, I mean :)
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