\(\Delta'=m^2-m+1=\left(m-\frac{1}{2}\right)+\frac{3}{4}>0\)
\(\Rightarrow\) Phương trình luôn có 2 nghiệm phân biệt \(\left\{{}\begin{matrix}x_1+x_2=2m\\x_1x_2=m-1\end{matrix}\right.\)
Từ điều kiện bài toán \(\Rightarrow\left\{{}\begin{matrix}x_1\ge0\\x_2\ge0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1+x_2>0\\x_1x_2\ge0\end{matrix}\right.\) \(\Rightarrow m\ge1\)
\(\sqrt{x_1}+\sqrt{x_2}=2\Leftrightarrow\left(\sqrt{x_1}+\sqrt{x_2}\right)^2=4\)
\(\Leftrightarrow x_1+x_2+2\sqrt{x_1x_2}=4\)
\(\Leftrightarrow2m+2\sqrt{m-1}=4\Leftrightarrow\sqrt{m-1}=2-m\)
\(\Leftrightarrow\left\{{}\begin{matrix}2-m\ge0\\m-1=\left(2-m\right)^2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}m\le2\\m^2-5m+5=0\end{matrix}\right.\) \(\Rightarrow m=\frac{5-\sqrt{5}}{2}\)
