Ta có : \(a^2+b^2+c^2-ab-ac-bc=0\)
=> \(2a^2+2b^2+2c^2-2ab-2ac-2bc=0\)
=> \(a^2+a^2+b^2+b^2+c^2+c^2-2ab-2ac-2bc=0\)
=> \(\left(a-b\right)^2+\left(a-c\right)^2+\left(b-c\right)^2=0\)
Ta thấy : \(\left\{{}\begin{matrix}\left(a-b\right)^2\ge0\\\left(a-c\right)^2\ge0\\\left(b-c\right)^2\ge0\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}a-b=0\\a-c=0\\b-c=0\end{matrix}\right.\)
=> a=b=c .
Ta có a2+b2+c2-ab-bc-ca=0
<=>2(a2+b2+c2-ab-bc-ca)=0
<=> (a-b)2+(b-c)2+(c-a)2=0
\(\Leftrightarrow\left\{{}\begin{matrix}a=b\\b=c\\c=a\end{matrix}\right.\)=> a=b=c
