Đáp án: $ A = \frac{254}{25}$
Giải thích các bước giải:
Theo Vi ét $: x_{1} + x_{2} = 2; x_{1}x_{2} = - 5$
$ ⇒ \frac{1}{x_{1}} + \frac{1}{x_{2}} = \frac{x_{1} + x_{2}}{x_{1}x_{2}} = - \frac{2}{5}$
$ \frac{1}{x_{1}²} + \frac{1}{x_{2}²} = (\frac{1}{x_{1}} + \frac{1}{x_{2}})² - \frac{2}{x_{1}x_{2}} = (- \frac{2}{5})² - \frac{2}{- 5} = \frac{14}{25}$
$ A = (\frac{1}{x_{1}} + 2)² + (\frac{1}{x_{2}} - 2)² - \frac{8}{x_{1}} $
$ = (\frac{1}{x_{1}²} + \frac{4}{x_{1}} + 4) + (\frac{1}{x_{2}²} - \frac{4}{x_{2}} + 4) - \frac{8}{x_{1}} $
$ = (\frac{1}{x_{1}²} + \frac{1}{x_{2}²}) - 4(\frac{1}{x_{1}} + \frac{1}{x_{2}}) + 8 $
$ = \frac{14}{25} - 4(- \frac{2}{5}) + 8 = \frac{254}{25}$
