$\sqrt {3{x^2} + (m - 1)x + (m - 4)}  \to x =  - 1$
$3{x^2} + (m - 1)x + m - 4 = 3{(x + 1)^2} = 3{x^2} + 6x + 3 \to $
$m - 1 = 6 \to m = 7$
$m - 4 = 3 \to m = 7$
$\frac{{\sqrt {3{{(x + 1)}^2}} }}{{\left| {1{x^3} + {\alpha ^2}} \right|}} \to x = \alpha  \to {\alpha ^3} + {\alpha ^2} = {\alpha ^2}(\alpha  + 1) = 0$
$ \to \begin{array}{*{20}{c}}
  {{\alpha ^2} = 0\,,\,\alpha  = 0\,\,\,\,\,\,\,\,\,\,\,} \\ 
  {\alpha  + 1 = 0 \to \alpha  =  - 1} 
\end{array}$
$\frac{{\sqrt {3 \times {{( - 1)}^2} + ( - 1 \times 6) + 3} }}{{1 - 1 + {{((7 - 7) \times ( - 1) + ( - 1))}^2}}} = \%  \to \lim \frac{{\sqrt 3 \left| {x + 1} \right|}}{{\left| {{x^3} + 1} \right|}} = \frac{{\sqrt 3 }}{3}$

تابع در $x = \alpha $ باید پیوسته باشد:

$f(\alpha ) = f( - 1) = \frac{{\sqrt 3 }}{3} \to \frac{{2\sin b}}{{3\sqrt { - 1 + 2} }} = \frac{{\sqrt 3 }}{3}$
$\sin b = \frac{{\sqrt 3 }}{2} \to b = \frac{\pi }{3}\,\,\,,\,\,\,{60^ \circ }$