Question

Решите систему уравнений:
{x²+y²+x+y=18
{x²-y²+x-y=6

Answer 1

$\left \{ {{x^2+y^2+x+y=18} \atop {x^2-y^2+x-y=6}} \right. \\ ------------\\ 2x^2+2x=24\\ \\x^2+x-12=0 \\ \\ D=49=7^2;x_{1} =-4;x_{2}= 3\\ \\ 1)x=-4\\ \\ 16+y^2-4+y=18\\ \\ y^2+y-6=0;(y-2)(y+3)=0\\ \\ y_{1} =-3;y_{2} =2\\ \\ (-4;-3)\ (-4;2)\\ \\ 2)x=3\\ \\ 9+y^2+3+y=18\\ \\y^2+y-6=0;(y-2)(y+3)=0\\ \\ y_{3} =-3;y_{4} =2\\ \\ (3;-3)\ (3;2)\\ \\ otvet: (-4;-3)\ (-4;2)\  (3;-3)\ (3;2)$