Решить систему {x^2 + x y + y^2 = 91, x + sqrt (x y) + y = 13}

{x^2+2xy+y^2 - xy=91,

x+√xy+y=13},

{ (x+y) ^2 - xy=91, (x+y) + √ (xy) = 13},

Делаем замену: x+y=p, √ (xy) = q,

{p^2 - q^2=91, p+q=13},

{ (p-q) (p+q) = 91, p+q=13},

{ (p-q) 13=91, p+q=13},

{p-q=7, p+q=13}, {p=10, q=3},

{x+y=10, √ (xy) = 3},{x+y=10, xy=9},

{x=10-y, (10-y) y=9},{x=10-y, y^2-10y+9=0}

{x=10-y, (y-9) (y-1) = 0},{x=10-y, y=9, y=1},

{x=1, y=9} или {x=9, y=1}