Question

Tìm m để hệ phương trình { 3x + y = m + 1
                                           { x - 2y = 5m - 2
có nghiệm (x ; y) thỏa mãn 4x² - y² = 10

Answer 1

\(\left\{{}\begin{matrix}3x+y=m+1\\x-2y=5m-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+2y=2m+2\\x-2y=5m-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7x=7m\\x-2y=5m-2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=m\\m-2y=5m-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=m\\y=1-2m\end{matrix}\right.\\ 4x^2-y^2=10\Leftrightarrow4m^2-\left(1-2m\right)^2=10\\ \Leftrightarrow4m^2-4m^2+4m-1=10\\ \Leftrightarrow m=\dfrac{11}{4}\)