$\text{Có $m^{2}-m+7=m^{2}-2.\frac{1}{2}m+7$}$
$\text{= $m^{2}-2.\frac{1}{2}m+\frac{1}{4}+\frac{27}{4}$}$
$\text{= $m^{2}-2.\frac{1}{2}m+(\frac{1}{2})^{2}+\frac{27}{4}$}$
$\text{= $(m-\frac{1}{2})^{2}+\frac{27}{4}$}$
$\text{Có $(m-\frac{1}{2})^{2}\geq0$ với mọi m}$
$\text{⇒ $(m-\frac{1}{2})^{2}+\frac{27}{4}\geq\frac{27}{4}>0$ với mọi m}$