\left \{ {{x+y=6} \atop {x\cdot y=-8}} \right.
\left \{ {{y=6-x} \atop {x\cdot (6-x) =-8}} \right.
-x^2+6x=-8 \ |*(-1)
(x^2-6x+9)-9=-8 \ |+9
(x-3)^2=17 pierwiastkuje obustronnie
|x=3|=\sqrt{17}
x-3=-\sqrt{17} \ \vee \ x-3=\sqrt{17}\\\\ x=3-\sqrt{17} \ \vee \ x=3+\sqrt{17}
dla x=3-\sqrt{17}
y=6-(3-\sqrt{17})=6-3+\sqrt{17}=3+\sqrt{17}
dla x=3+\sqrt{17}
y=6-(3+\sqrt{17})=6-3-\sqrt{17}=3-\sqrt{17}
Odpowiedź:
Szukane liczby to 3-\sqrt{17} i 3+\sqrt{17}.