\(a;\)\(pt\) \(hoành\) \(độ\) \(giao\) \(điểm:x^2=mx-2m+4\)
\(\Leftrightarrow x^2-mx+2m-4=0\)
\(\Delta>0\)\(\Leftrightarrow m^2-4\left(2m-4\right)>0\Leftrightarrow m^2-8m+16>0\Leftrightarrow\left(m-4\right)^2>0\Leftrightarrow m\ne4\)
\(b;vi\) \(ét\Rightarrow\left\{{}\begin{matrix}x1+x2=m\\x1x2=2m-4\end{matrix}\right.\)
\(điều\) \(kiện\) \(tồn\) \(tại\) \(căn:0\le x1< x2\Leftrightarrow\left\{{}\begin{matrix}x\ne4\\x1.x2\ge0\\x1+x2>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne4\\m\ge2\\m>0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}m\ne4\\m\ge2\end{matrix}\right.\)
\(\Rightarrow\sqrt{x1}+\sqrt{x2}=3\sqrt{2}\)
\(\Leftrightarrow x1+x2+2\sqrt{x1x2}=18\)
\(\Leftrightarrow m+2\sqrt{2m-4}-18=0\left(1\right)\)
\(đặt:\sqrt{2m-4}=t\ge0\Rightarrow\left(1\right)\Leftrightarrow\dfrac{t^2+4}{2}+2t-18=0\Leftrightarrow t^2+4+4t-36=0\Leftrightarrow\left[{}\begin{matrix}t=4\left(tm\right)\\t=-8\left(loại\right)\end{matrix}\right.\)
\(t=4=\sqrt{2m-4}\Leftrightarrow m=10\left(tm\right)\)
