Đáp án: m=3,8 hoặc m=5
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
x + y = 5\\
\left( {m - 2} \right)x + \left( {m - 4} \right)y = 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
\left( {m - 2} \right)x + \left( {m - 2} \right)y = 5\left( {m - 2} \right)\\
\left( {m - 2} \right)x + \left( {m - 4} \right)y = 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x + y = 5\\
2y = 5\left( {m - 2} \right) - 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = 5 - y\\
y = \dfrac{{5m - 17}}{2}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = \dfrac{{27 - 5m}}{2}\\
y = \dfrac{{5m - 17}}{2}
\end{array} \right.\\
Dkxd:x \ge 0;y \ge 0\\
\Rightarrow \left\{ \begin{array}{l}
27 - 5m \ge 0\\
5m - 17 \ge 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
m \le \dfrac{{27}}{5}\\
m \ge \dfrac{{17}}{5}
\end{array} \right.\\
\Rightarrow 3,2 \le m \le 5,2\\
Do:\sqrt x + \sqrt y = 3\\
\Rightarrow x + 2\sqrt {xy} + y = 9\\
\Rightarrow 5 + 2\sqrt {xy} = 9\\
\Rightarrow 2\sqrt {xy} = 4\\
\Rightarrow \sqrt {xy} = 2\\
\Rightarrow x.y = 4\\
\Rightarrow \dfrac{{5m - 17}}{2}.\dfrac{{27 - 5m}}{2} = 4\\
\Rightarrow - 25{m^2} + 135m + 85m - 17.27 - 16 = 0\\
\Rightarrow 25{m^2} - 220m + 475 = 0\\
\Rightarrow \left( {5m - 25} \right)\left( {5m - 19} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
m = 5\\
m = \dfrac{{19}}{5} = 3,8
\end{array} \right.\left( {tmdk} \right)
\end{array}$
