Đáp án:

$C1:\left( {x;y} \right) = \left( {0;3} \right)$

$C2:a)A = \dfrac{1}{{x - 1}},x \ge 0;x \ne 1$$;b)m = \dfrac{{28 - \sqrt {37} }}{3}$

Giải thích các bước giải:

$\begin{array}{l}
C1:\\
b)\left\{ \begin{array}{l}
2x + y - 3 = 0\\
\dfrac{x}{4} = \dfrac{y}{3} - 1
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
2x + y = 3\\
3x - 4y =  - 12
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
x = 0\\
y = 3
\end{array} \right.
\end{array}$

$\begin{array}{l}
C2:\\
a)DKXD:x \ge 0;x \ne 1\\
A = \left( {\dfrac{{2\sqrt x  + x}}{{x\sqrt x  - 1}} - \dfrac{1}{{\sqrt x  - 1}}} \right):\left( {1 - \dfrac{{\sqrt x  + 2}}{{x + \sqrt x  + 1}}} \right)\\
 = \left( {\dfrac{{2\sqrt x  + x}}{{\left( {\sqrt x  - 1} \right)\left( {x + \sqrt x  + 1} \right)}} - \dfrac{1}{{\sqrt x  - 1}}} \right):\dfrac{{x + \sqrt x  + 1 - \left( {\sqrt x  + 2} \right)}}{{x + \sqrt x  + 1}}\\
 = \dfrac{{2\sqrt x  + x - \left( {x + \sqrt x  + 1} \right)}}{{\left( {\sqrt x  - 1} \right)\left( {x + \sqrt x  + 1} \right)}}.\dfrac{{x + \sqrt x  + 1}}{{x - 1}}\\
 = \dfrac{{\sqrt x  - 1}}{{\left( {\sqrt x  - 1} \right)\left( {x + \sqrt x  + 1} \right)}}.\dfrac{{x + \sqrt x  + 1}}{{x - 1}}\\
 = \dfrac{1}{{x - 1}}
\end{array}$

b) Ta có:

Phương trình ${x^2} - 5x + m - 3 = 0$ có 2 nghiệm $x_1;x_2$ phân biệt

$\begin{array}{l}
 \Leftrightarrow \Delta  > 0\\
 \Leftrightarrow {\left( { - 5} \right)^2} - 4.1.\left( {m - 3} \right) > 0\\
 \Leftrightarrow m - 3 < \dfrac{{25}}{4}\\
 \Leftrightarrow m < \dfrac{{37}}{4}
\end{array}$

Theo ĐL Viet ta có: $\left\{ \begin{array}{l}
{x_1} + {x_2} = 5\\
{x_1}{x_2} = m - 3
\end{array} \right.$

Khi đó;

$\begin{array}{l}
x_1^2 - 2{x_1}{x_2} + 3{x_2} = 1\\
 \Leftrightarrow 5{x_1} - m + 3 - 2{x_1}{x_2} + 3{x_2} = 1\\
 \Leftrightarrow 5{x_1} + 3{x_2} - m + 3 - 2\left( {m - 3} \right) = 1\\
 \Leftrightarrow 5{x_1} + 3{x_2} = 3m - 8
\end{array}$

Lại có: 

$\begin{array}{l}
{x_1} + {x_2} = 5\\
 \Rightarrow {x_1} = \dfrac{{3m - 23}}{2};{x_2} = \dfrac{{33 - 3m}}{2}
\end{array}$

Như vậy:

$\begin{array}{l}
{x_1}{x_2} = m - 3\\
 \Leftrightarrow \left( {\dfrac{{3m - 23}}{2}} \right)\left( {\dfrac{{33 - 3m}}{2}} \right) = m - 3\\
 \Leftrightarrow 9{m^2} - 168m + 747 = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
m = \dfrac{{28 + \sqrt {37} }}{3}\left( l \right)\\
m = \dfrac{{28 - \sqrt {37} }}{3}\left( c \right)
\end{array} \right.
\end{array}$

$ \Leftrightarrow m = \dfrac{{28 - \sqrt {37} }}{3}$