Question

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

tìm m để hệ có nghiệm duy nhất (x,y) sao cho \(y-\sqrt{x}=1\)

Answer 1

Vì \(\dfrac{3}{1}\ne\dfrac{-1}{2}\)

nên hệ luôn có nghiệm duy nhất

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

=>\(\left\{{}\begin{matrix}3x-y=2m-1\\3x+6y=9m+6\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-7y=2m-1-9m-6=-7m-7\\x+2y=3m+2\end{matrix}\right.\)

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

\(y-\sqrt{x}=1\)

=>\(m+1-\sqrt{m}=1\)

=>\(m-\sqrt{m}=0\)

=>\(\sqrt{m}\left(\sqrt{m}-1\right)=0\)

=>\(\left[{}\begin{matrix}m=0\\m=1\end{matrix}\right.\)