Question

Решите пожалуйста.............

Answer 1

$\begin{cases}x^3-y^3=218,\\ x^2+xy+y^2=109;\end{cases}\,\begin{cases}(x-y)(x^2+xy+y^2)=218,\\ x^2+xy+y^2=109;\end{cases}\\ \begin{cases}x-y=2,\\ x^2+xy+y^2=109;\end{cases}\,\begin{cases}x=y+2,\\ (y+2)^2+(y+2)y+y^2=109;\end{cases}\\ y^2+4y+4+y^2+2y+y^2=109;\\ 3y^2+6y-105=0;\,|:3\\ y^2+2y-35=0;\\ \begin{cases}y_1=5,\\ x_1=7;\end{cases}\, \begin{cases}y_2=-7,\\ x_2=-5.\end{cases}\,$