M thuộc (P) nên \(M\left(x_1;-x_1^2+4x_1+5\right)\)
N thuộc (P) nên \(N\left(x_2;-x_2^2+4x_2+5\right)\)
Theo đề, ta có hệ:
\(\left\{{}\begin{matrix}x_1+x_2=2\\-x_1^2+4x_1+5-x_2^2+4x_2+5=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x_1=2-x_2\\-\left(2-x_2\right)^2+4\left(2-x_2\right)+5-x_2^2+4x_2+5=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x_1=2-x_2\\-x_2^2+4x_2-4+8-4x_2+5-x_2^2+4x_2+5=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x_1=8-x_2\\-2x_2^2+4x_2+6=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1=8-x_2\\x_2\in\left\{3;-1\right\}\end{matrix}\right.\)
=>\(\left(x_1;x_2\right)\in\left\{\left(5;3\right);\left(9;-1\right)\right\}\)
=>\(\left(y_1;y_2\right)\in\left\{\left(0;8\right);\left(-40;0\right)\right\}\)
