Question

( 3x − y = 2m − 1
(x + 2y = 3m + 2.

 hãy tìm m để hệ có nghiệm (x;y) thõa mãn x2 + y2 = 10.

Answer 1

\(\left\{{}\begin{matrix}3x-y=2m-1\\x+2y=3m+2\end{matrix}\right.\)

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

\(x^2+y^2=10\)

\(\Leftrightarrow m^2+\left(m+1\right)^2=10\)

\(\Leftrightarrow2m^2+2m-9=0\)

\(\Leftrightarrow\left[{}\begin{matrix}m=\dfrac{-1+\sqrt{19}}{2}\\m=\dfrac{-1-\sqrt{19}}{2}\end{matrix}\right.\)