$7x² + 14x - 21 = 0$
$\text{ Ta có: $Δ = 14² + 4.21.7 . 0$ ∀x ∈R}$
$\text{ Do đó PT luôn có 2 nghiệm PB}$
$\text{ Ta có hệ thức Vi - ét: }$
$\left\{\begin{matrix}x_{1}+x_{2}=-2\\x_{1}.x_{2}=-3\end{matrix}\right.$
$\text{ Theo đề bài:}$
$A= \dfrac{x_{2}+3}{x_{1}} + \dfrac{x_{1}+3}{x_{2}}$
$= \dfrac{x_{2}(x_{2}+3)}{x_{1}x_{2}} + \dfrac{x_{1}(x_{1}+3)}{x_{1}x_{2}}$
$= \dfrac{x_{2}² + 3x_{2} + x_{1}² + 3x_{1}}{x_{1}x_{2}}$
$= \dfrac{(x_{1}+x_{2})²-2x_{1}x_{2}+3(x_{1} + x_{2})}{x_{1}x_{2}}$
$= \dfrac{(-2)²-2(-3)+3(-2)}{-3}$
$= \dfrac{-4}{3}$
$\text{ Vậy $A = \dfrac{-4}{3}$}$
