Verified answer

Ответ: 30 и 11.

Объяснение:

Пусть искомые числа равны х и у.         ⇒

[tex]\displaystyle\\\left \{ {{x-y=19} \atop {x^2-y^2=779}} \right.\ \ \ \ \left \{ {{x-y=19} \atop {(x-y)*(x+y)=779}} \right. \ \ \ \ \left \{ {{x-y=19} \atop {19*(x+y)=779\ |:19}} \right. \\\\\\+\left \{ {{x-y=19} \atop {x+y=41}} \right. \ \ \ \ \Rightarrow\ \ \ \ 2x=60\ |:2\ \ \ \ x=30\\\\\\30-y=19\\\\-y=-11\ |*(-1)\\\\y=11.[/tex]