Question

ПОМОГИТЕ ПЛИИС!!! ДАЮ 90 БАЛЛОВ

Answer 1

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