\(\text{Δ}=\left(-4\right)^2-4\cdot1\cdot\left(m+2\right)=16-4m-8=-4m+8\)
Để phương trình có nghiệm thì Δ>=0
=>-4m+8>=0
=>-4m>=-8
=>m<=2
Theo Vi-et, ta có:
\(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=4\\x_1x_2=\dfrac{c}{a}=m+2\end{matrix}\right.\)
Theo đề, ta có hệ:
\(\left\{{}\begin{matrix}x_1+x_2=4\\x_1-x_2=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x_1=10\\x_1+x_2=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x_1=5\\x_2=-1\end{matrix}\right.\)
\(x_1x_2=m+2\)
=>m+2=-5
=>m=-7(nhận)