\(a,\\ \Delta'=\left(m-3\right)^2+2\left(m+4\right)=m^2-6m+9+2m+8\\ =m^2-4m+17=m^2-4m+4+13\\ =\left(m-2\right)^2+13\\ Có.\left(m-2\right)^2+13\ge13\forall m\\ \Rightarrow\Delta'.luôn.>0\forall m\\ \Rightarrow......_{\left(đpcm\right)}\\ b,\\ x=1.là.nghiệm\\ \Rightarrow\left(m+4\right).1^2-2\left(m-3\right)-0.1-2=0\\ \Rightarrow\left(m+4\right)-2m+6-2=0\\ \Leftrightarrow8-m=0\Rightarrow m=8\)
Theo Vi ét
\(x_1x_2=\dfrac{-2}{m+4}=\dfrac{-2}{8+4}=\dfrac{-1}{6}\\ \Rightarrow x_2=1.\dfrac{-1}{6}=\dfrac{-1}{6}\)
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