Ta có: \(\left\{{}\begin{matrix}x_1+x_2=m+1\\x_1x_2=m-4\end{matrix}\right.\Rightarrow m=x_1+x_2-1\)
Khi đó: \(\left(x_1^2-mx_1+m\right)\left(x_2^2-mx_2+m\right)=2\)
\(\Leftrightarrow\left[x_1^2-\left(x_1+x_2-1\right)x_1+m\right]\left[x_2^2-\left(x_1+x_2-1\right)x_2+m\right]=2\)
\(\Leftrightarrow\left(x_1-x_1x_2+m\right)\left(x_2-x_1x_2+m\right)=2\)
\(\Leftrightarrow\left[x_1-\left(m-4\right)+m\right]\left[x_2-\left(m-4\right)+m\right]=2\)
\(\Leftrightarrow\left(x_1+4\right)\left(x_2+4\right)=2\)
\(\Leftrightarrow x_1x_2+4\left(x_1+x_2\right)+16=2\)
\(\Leftrightarrow m-4+4\left(m+1\right)=-14\)
\(\Leftrightarrow5m=-14\)
\(\Leftrightarrow m=-\dfrac{14}{5}\)
$\text{#}Toru$
