Cho hệ phương trình

- Hướng dẫn giải

Ta có $\left\{\begin{array}{l}2x+y=5m-1\\ x-2y=2\end{array}\right.$

$\iff \left\{\begin{array}{l}y=5m-1-2x\\ x-2\left(5m-1-2x\right)=2\end{array}\right.\iff \left\{\begin{array}{l}y=5m-1-2x\\ 5x=10m\end{array}\right.$

$\iff \left\{\begin{array}{l}x=2m\\ y=m-1\end{array}\right.$

Thay vào $x^2 – 2y^2 = -2$ ta có

$$\begin{gathered} x^2–2y^2=-2\iff {\left(2m\right)}^2–2{(m-1)}^2 =-2 \\ \iff 2m^2+4m=0\iff \left[\begin{array}{l}m=0\\ m=-2\end{array}\right. \end{gathered}$$    

Vậy m $\in${−2; 0}

Đáp án: C