Bài 2.
a.\(\Delta=\left(-6\right)^2-4.8=36-32=4>0\)
=> pt luôn có 2 nghiệm phân biệt
b.Theo hệ thức Vi-ét, ta có:
\(\left\{{}\begin{matrix}x_1+x_2=6\\x_1.x_2=8\end{matrix}\right.\)
\(A=x_1^2+x_2^2-4x_1-4x_2\)
\(A=\left(x_1+x_2\right)^2-2x_1.x_2-4\left(x_1+x_2\right)\)
\(A=6^2-2.8-4.6=-4\)
Bài 3. Theo hệ thức Vi-ét, ta có:
\(\left\{{}\begin{matrix}x_1+x_2=3\\x_1.x_2=-2\end{matrix}\right.\)
\(\dfrac{x_1}{x_2}+\dfrac{x_2}{x_1}=\dfrac{x_1.x_1+x_2.x_2}{x_1.x_2}=\dfrac{x_1^2+x_2^2}{x_1.x_2}=\dfrac{\left(x_1+x_2\right)^2-2x_1.x_2}{x_1.x_2}=\dfrac{3^2-2.-2}{-2}=\dfrac{13}{-2}=-\dfrac{13}{2}\)
