a/ $x^2-12x+37$
$= x^2-12x+36 +1 $
$= (x-6)^2+1 \ge 1 >0 \;\forall x$
b/ $a^2+b^2+c^2=ab+bc+ca$
$⇔ 2a^2+2b^2+c^2=2ab+2bc+2ac$
$⇔ (a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ac+a^2)=0$
$⇔ (a-b)^2+(b-c)^2+(c-a)^2=0$
$⇔ \begin{cases}a-b=0\\b-c=0\\c-a=0\end{cases}$
$⇔ \begin{cases}a=b\\b=c\\c=a\end{cases}$
$⇔ a=b=c$ (đpcm)