a. Ta có: \(\Delta=5^2-4.3.\left(-6\right)=97>0\)
Định lí Vi - et ta có:
\(\left\{{}\begin{matrix}x_1+x_2=\dfrac{-b}{a}=\dfrac{-5}{3}\\x_1.x_2=\dfrac{c}{a}=\dfrac{-6}{3}=-2\end{matrix}\right.\)
Theo đề bài ta có:
\(A=\dfrac{x_1}{\left(x_2-1\right)}+\dfrac{x_2}{\left(x_1-1\right)}\)
\(=\dfrac{x_1\left(x_1-1\right)}{\left(x_1-1\right)\left(x_2-1\right)}+\dfrac{x_2\left(x_2-1\right)}{\left(x_1-1\right)\left(x_2-1\right)}\)
\(=x_1\left(x_1-1\right)+x_2\left(x_2-1\right)\)
\(=x^2_1-x_1+x^2_2-x_2\)
\(=x^2_1+x_2^2+2x_1x_2-2x_1x_2-x_1-x_2\)
\(=\left(x_1+x_2\right)^2-2x_1x_2-x_1-x_2\)
\(=\left(x_1+x_2\right)^2-2x_1x_2-1\left(x_1+x_2\right)\)
\(=\left(\dfrac{-5}{3}\right)^2-2.\left(-2\right)-1\left(\dfrac{-5}{3}\right)\)
\(=\dfrac{76}{9}\)
