Question

Система уравнений
{1/x-1/y=1/6
{x*y=6

Answer 1

$left { {{ frac{1}{x}- frac{1}{y}= frac{1}{6} } atop {xy=6}} right.$
ОДЗ: $x neq 0,$   $y neq 0$
$left { {{ frac{y-x}{xy}}= frac{1}{6} } atop {xy=6}} right.$
$left { {{{6(y-x)}{=xy}} } atop {xy=6}} right.$
$left { {{{6(y-x)}{=6}} } atop {xy=6}} right.$
$left { {y-x}{=1}} } atop {xy=6}} right.$
$left { {y}{=1+x}} } atop {x(1+x)=6}} right.$
$left { {y}{=1+x}} } atop {x^2+x-6=0}} right.$
$x^{2} +x-6=0$
$D=1^2-4*1*(-6)=25$
$x_1= frac{-1+5}{2} =2,$         $y_1=2+1=3$
$x_2= frac{-1-5}{2} =-3,$      $y_2=-3+1=-2$

Ответ: (2;3);  (-3;-2)