Question

Помогите решить :
$left { {{ x^{3}- y^{3} =28 } atop { x^{2} +xy+ y^{2} =7}} right.$

Answer 1

(x-y)(x²+xy+y²)=28⇒(x-y)*7=28⇒x-y=4⇒x=y+4
(y+4)²+y(y+4)+y²-7=0
y²+8y+16+y²+4y+y²-7=0
3y²+12y+9=0
y²+4y+3=0
y1+y2=-4 U y1*y2=3
y1=-3 x1=-3+4=1
y2=-1 x2=-1+4=3
Ответ (1;-3) и (3;-1)

Answer 2

x^3-y^3=(x-y)*(x^2+xy+y^2)=28
(x^2+xy+y^2)=7
*************
28=(x-y)*7
(x^2+xy+y^2)=7
*************
(x-y)=4
(x^2+xy+y^2)=(x-y)^2+3xy=4^2+3xy=7
*************
(x-y)=4
16+3xy=7
*************
(x-y)=4
xy=-3
*************
x=4+y
y^2+4y+3=0
*************
y1=-1; x1=4+y1=3
y2=-3; x2=4+y2=1
*************
ответ (3;-1) и (1;-3)