Question

Решите систему $left { {{x^2 + xy +y^2=37} atop {x^3 - y^3=37}} right.$

Answer 1

$left { {{x^2+xy+y^2=37} atop {x^3-y^3=37}} right. \ \left { {{x^2+xy+y^2=37} atop {(x-y)(x^2+xy+y^2)=37}} right.  \ \ x-y=1\ \ x=y+1\ \ (y+1)^2+(1+y)y+y^2=37$

$1+2y+y^2+y+y^2+y^2=37\ \ 3y^2+3y-36=0\ \ y^2+y-12=0\ \ D=49$

$y_{1} =(-1-7)/2=-4;x_{1} =-4+1=-3\ \ y_{2} =(-1+7)/2=3;x_{2} =3+1=4 \ \ otvet:(-3;-4)(4;3)$