Question

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

Answer 1

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

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

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