Question

ai giúp vs ạ,tí nộp r

\(\left\{{}\begin{matrix}2\text{x}+y=5m-1\\x-2y=2\end{matrix}\right.\)(m là tham số)

tìm m để pt có 2 nghiệm thỏa mãn \(x^2-2y^2=-2\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}4x+2y=10m-2\\x-2y=2\end{matrix}\right.\) \(\Rightarrow5x=10m\Rightarrow x=2m\)

\(\Rightarrow y=5m-1-2x=m-1\)

\(x^2-2y^2=-2\Leftrightarrow\left(2m\right)^2-2\left(m-1\right)^2=-2\)

\(\Leftrightarrow4m^2-2m^2+4m-2+2=0\)

\(\Leftrightarrow2m^2+4m=0\Leftrightarrow2m\left(m+2\right)=0\Rightarrow\left[{}\begin{matrix}m=0\\m=-2\end{matrix}\right.\)