\(\left(t-1\right)\left(t+1\right)-m\left(t-1\right)=0\)
\(\Leftrightarrow\left(t-1\right)\left(t-m+1\right)=0\Rightarrow\left[{}\begin{matrix}t=1\\t=m-1\end{matrix}\right.\)
a.
TH1: \(\left\{{}\begin{matrix}t_1=1\\t_2=m-1\end{matrix}\right.\) \(\Rightarrow1=3\left(m-1\right)\Rightarrow m=\frac{4}{3}\)
TH2: \(\left\{{}\begin{matrix}t_1=m-1\\t_2=1\end{matrix}\right.\) \(\Rightarrow m-1=3.1\Rightarrow m=4\)
b.
\(A=\left(t_1+t_2\right)^2-8t_1t_2=m^2-8\left(m-1\right)\)
\(A=m^2-8m+8=\left(m-4\right)^2-8\ge-8\)
\(A_{min}=-8\) khi \(m=4\)
