Ответ: {x²+y²-xy=31⇒(x-y)²+xy=31{x²y-xy²=-30⇒xy(x-y)=-30делаем замену x-y=a,xy=b{a²+b=31⇒b=31-a²{ab=-30⇒(31-a²)a=-30a³-31a-30=0a²(a+1)-a(a+1)-30(a+1)=0(a+1)(a²-a-30)=0(a+1)(a(a-6)+5(a-6))=0(a+1)(a+5)(a-6)=01)a+1=0⇒a=-1 b=31-1=30{x-y=-1⇒x=y-1{xy=30y²-y-30=0y1+y2=1 U y1*y2=-30y1=6 x1=6-1=5y2=-5 x2=-5-1=-62)a+5=0⇒a=-5 b=31-25=6{x-y=-5⇒x=y-5{xy=6y²-5y-6=0y1+y2=5 U y1*y2=-6y1=6 x1=6-5=1y2=-1 x2=-1-5=-63)a=6 b=31-36=-5{x-y=6⇒y+6{xy=-5y²+6y+5=0y1+y2=-6 U y1*y2=5y1=-1 x1=-1+6=5y2=-5 x2=-5+6=1Ответ (5;6);(-6;-5);(1;6);(-6;-1);(5;-1);(1;-5)
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