Đáp án:
b. \(\left\{ \begin{array}{l}
y = 4 - 2\sqrt 2 \\
x = 8 - 4\sqrt 2
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
mx + 4y = 8\\
x + my = 4
\end{array} \right.\\
a.m = 1\\
Hpt \to \left\{ \begin{array}{l}
x + 4y = 8\\
x + y = 4
\end{array} \right.\\
\to \left\{ \begin{array}{l}
4y - y = 8 - 4\\
x + y = 4
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \frac{4}{3}\\
x = \frac{8}{3}
\end{array} \right.\\
b.m = \sqrt 2 \\
\to \left\{ \begin{array}{l}
x\sqrt 2 + 4y = 8\\
x + \sqrt 2 y = 4
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x\sqrt 2 + 4y = 8\\
x\sqrt 2 + 2y = 4\sqrt 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
4y - 2y = 8 - 4\sqrt 2 \\
x\sqrt 2 + 4y = 8
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 4 - 2\sqrt 2 \\
x = 8 - 4\sqrt 2
\end{array} \right.\\
c.\left\{ \begin{array}{l}
mx + 4y = 8\\
x + my = 4
\end{array} \right.\\
\to \left\{ \begin{array}{l}
mx + 4y = 8\\
mx + {m^2}y = 4m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {4 - {m^2}} \right)y = 4\left( {2 - m} \right)\\
mx + 4y = 8
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \frac{{4\left( {2 - m} \right)}}{{\left( {2 - m} \right)\left( {2 + m} \right)}}\\
x = \frac{{8 - 4y}}{m}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \frac{4}{{m + 2}}\\
x = \frac{{8m + 16 - 16}}{{m\left( {m + 2} \right)}} = \frac{8}{{m + 2}}
\end{array} \right.
\end{array}\)
Để hpt có nghiệm
\( \Leftrightarrow m + 2 \ne 0 \to m \ne - 2\)
Để hpt vô nghiệm
\( \Leftrightarrow m + 2 = 0 \to m = - 2\)
