`A = (x_1 + 1 + x_2 + 1)/(x_1x_2 + x_1+x_2 + 1)`
`= (x_1 + x_2 + 2)/(x_1x_2 + x_1 + x_2 + 1)`.
Mà theo hệ thức Viet: {(x_1 + x_2 = -b/a = 2/3), (x_1x_2 =c/a -1/3):}`
A = (2/3 + 2)/(-1/3 + 2/3 + 1)`
`= 8/3 : 4/3`
`= 2`.
\(\Delta=b^2-4ac=\left(-2\right)^2-4.3.\left(-1\right)=16>0\)
\(\Rightarrow\) Pt có 2 nghiệm pb
\(\left\{{}\begin{matrix}x_1=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{2+4}{2.3}=1\\x_2=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{2-4}{2.3}=-\dfrac{1}{3}\end{matrix}\right.\)
Ta có :
\(\left\{{}\begin{matrix}S=x_1+x_2=1-\dfrac{1}{3}=\dfrac{2}{3}\\P=x_1x_2=1.\left(-\dfrac{1}{3}\right)=-\dfrac{1}{3}\end{matrix}\right.\)
\(A=\dfrac{1}{x_2+1}+\dfrac{1}{x_1+1}\)
\(=\dfrac{x_1+1+x_2+1}{\left(x_2+1\right)\left(x_1+1\right)}\)
\(=\dfrac{x_1+x_2+2}{x_1x_2+x_2+x_1+1}\)
\(=\dfrac{S+2}{P+S+1}\)
\(=\dfrac{\dfrac{2}{3}+2}{-\dfrac{1}{3}+\dfrac{2}{3}+1}\)
\(=2\)
