Question

решите уравнение (x-4)/(x+2)+(x+2)/(x-4)=17/4

Answer 1

$frac{x-4}{x+2}+ frac{x+2}{x-4}= frac{17}{4} \ frac{(x-4)^{2}+(x+2)^{2}}{(x+2)(x-4)}- frac{17}{4} =0\ frac{4(x-4)^{2}+4(x+2)^{2}-17(x+2)(x-4)}{4(x+2)(x-4)} =0\ frac{(2*(x-4))^{2}-2*2*2*(x+2)(x-4)+(2*(x+2))^{2}-9(x+2)(x-4)}{4(x+2)(x-4)} =0\ frac{(2(x-4)-2(x+2))^{2}-9(x+2)(x-4)}{4(x+2)(x-4)} =0\ frac{(2x-8-2x-4))^{2}-9(x^{2}-2x-8)}{4(x+2)(x-4)} =0\ frac{144-9x^{2}+18x+72)}{4(x+2)(x-4)} =0\ x^{2}-2x-24=0 \ x neq -2 \ x neq 4 \ D=4+96=100 \ x_{1}=frac{2+10}{2}=6$
$x_{2}=frac{2-10}{2}=-4$
Ответ: 6; -4

Answer 2

спасибо большое)))