Xét
$\displaystyle\lim _{x\rightarrow 5^{+}} f( x) =\displaystyle\lim _{x\rightarrow 4^{+}}\dfrac{2x-10}{3-\sqrt{2x-1}}$
$=\displaystyle\lim _{x\rightarrow 5^{+}}\dfrac{( 2x-10)\left( 3+\sqrt{2x-1}\right)}{10-2x} =\displaystyle\lim _{x\rightarrow 5^{+}} -\left( 3+\sqrt{2x-1}\right) $
$=-6$
$\displaystyle\lim _{x\rightarrow 5^{-}} f( x) =\displaystyle\lim _{x\rightarrow 5^{-}}\left[( x-5)^{2} +mx\right] = 5m$
Để $f( x)$ liên tục tại $x=5$
$\Leftrightarrow \displaystyle\lim _{x\rightarrow 5^{+}} f( x) =\displaystyle\lim _{x\rightarrow 5^{-}} f( x) =f( 5) \Leftrightarrow 5m-6\Leftrightarrow m=-\dfrac{6}{5}$
Vậy m=-$\dfrac{6}{5}$.
