Question

Решить систему уравнений

Answer 1

{х³+у³=19
{(ху+8)(х+у)=2
(х+у)(х²-ху+у²)=19
х+у=a
xy=b
x²+y²=(x+y)²-2xy=a²-2b
{a(a²-3b)=19
{(b+8)•a=2
ab+8a=2
ab=2-8a
a³-3ab=19
a³-3(2-8a)=19
a³-6+24a-19=0
a³-25+24a=0
a³-a+25a-25=0
a(a-1)(a+1)+25(a-1)=0
(a-1)(a²+a+25)=0
1)a-1=0;a=1
2)a²+a+25=0 ;a€∅
ab=2-8a
b=2-8=-6
{x+y=1;x=1-y
{xy=-6;(1-y)y=-6
-y²+y+6=0
y²-y-6=0
D=1+24=25=5²
y=(1±5)/2
y1=3;y2=-2
x1=1-y=1-3=-2
x2=1-(-2)=3
ответ (-2;3);(3;-2)