x^2+y^2+xy = (x+y)^2-xy = 91 x+y+sqrt(x)*sqrt(y) = (sqrt(x)+sqrt(y))^2-sqrt(x)*sqrt(y) = 13
Замена sqrt(x)=a, sqrt(y)=b
{(a^2+b^2)^2-a^2*b^2=91
{(a+b)^2-a*b=13
a^2+b^2=(a+b)^2-2ab
Вторая замена a+b=n, a*b=m
{(n^2-2m)^2-m^2=91
{n^2-m=13
(13-m)^2-m^2=91
169-26m=91
26m=169-91
m=3, n=4
{sqrt(x)+sqrt(y)=4
{sqrt(x)*sqrt(y)=3
sqrt(x)*(4-sqrt(x))=3
t(4-t)=3
t^2-4t+3=0
t = (4+-2)/2 = 1 и 3
x=1 и x=9
y=9, y=1
Ответ (1,9) и (9,1)