Đáp án:
-1<m<1
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x + y = m\\
x - y = 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = y + 1\\
y + 1 + y = m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{m - 1}}{2}\\
x = \dfrac{{m - 1 + 2}}{2} = \dfrac{{m + 1}}{2}
\end{array} \right.\\
\end{array}\)
Do hệ phương trình có 2 nghiệm trái dấu
\(\begin{array}{l}
\to x.y < 0\\
\to \dfrac{{m - 1}}{2}.\dfrac{{m + 1}}{2} < 0\\
\to \left( {m - 1} \right)\left( {m + 1} \right) < 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
m - 1 > 0\\
m + 1 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
m - 1 < 0\\
m + 1 > 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
m > 1\\
m < - 1
\end{array} \right.\left( l \right)\\
\left\{ \begin{array}{l}
m < 1\\
m > - 1
\end{array} \right.
\end{array} \right.\\
\to - 1 < m < 1
\end{array}\)
