1. \(x^2-5x+6=0\Leftrightarrow x^2-2x-3x+6=0\)
\(\Leftrightarrow x\left(x-2\right)-3\left(x-2\right)=0\Leftrightarrow\left(x-2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}x-2y=3\\3x+y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-2y=3\\6x+2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7x=7\\x-2y=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)
4. \(x^2+2y^2+2xy-6y+2027=\left(x^2+2xy+y^2\right)+\left(y^2-6y+9\right)+2018\)
\(=\left(x+y\right)^2+\left(y-3\right)^2+2018\ge2018\)
\(\Rightarrow A_{min}=2018\)
Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}x+y=0\\y-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=3\end{matrix}\right.\)
3:
a: Xét tứ giác MAOB có
góc MAO+góc MBO=180 độ
=>MAOB nội tiếp
b: Xét ΔMAC và ΔMDA có
góc MAC=góc MDA
góc AMC chung
=>ΔMAC đồng dạng với ΔMDA
