Question

помогите решить систему уравнений.

Answer 1

$left { {{x^2+y^2+xy=7} atop {x^2y-xy^2=30}} right. ; left { {{(x-y)^2+3xy=7} atop {xy(x-y)=30}} right. ; left { {{(x-y)^2+3cdot frac{30}{x-y}-7=0} atop {xy=frac{30}{x-y}} right. \\t=x-y; ,; ; t^2+frac{90}{t}-7=0\\t^3-7t+90=0; ,; tne 0\\Pri; ;t=-5:; ; (-5)^3-7(-5)+90=0; ; to \\t^3-7t+90=(t+5)(t^2-5t+18)\\t^2-5t+18=0; ,; ; D=25-4cdot 18=-47 textless 0; ; to t^2-5t+18 textgreater 0\\(t+5)(t^2-5t+18)=0; ; to ; ; t=-5\\x-y=-5; ; to ; ; y=x+5$

$x^2+y^2+xy=x^2+(x+5)^2+x(x+5)=7\\3x^2+15x+18=0; |:3\\x^2+5x+6=0\\x_1=-3; ,; x_2=-2; ; (teorema; Vieta)\\y_1=-3+5=2; ,; y_2=-2+5=3\\Otvet:; ; (-3;2); ,; (-2;3); .$