Question

giải hệ ptr

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

Answer 1

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)^2=2y+2\\y=-\dfrac{5}{9}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)^2=\dfrac{8}{9}\\y=-\dfrac{5}{9}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-1=\pm\dfrac{2\sqrt{2}}{3}\\y=-\dfrac{5}{9}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=1\pm\dfrac{2\sqrt{2}}{3}\\y=-\dfrac{5}{9}\end{matrix}\right.\)