Question

Решите систему
х-у=2
х^3-y^3=56

Answer 1

x=2+y
(2+y)^3-y^3=56


(4+4y+y^2)(y+2)-y^3=56
4y+4y^2+8+8y+2y^2=56
6y^2+12y-48=0
y^2+2y-8=0
D=4+32=36
y=(-2+6)/2=2
y=-8/2=-4
x-(-4)=2
x=-2
x-2=2
x=4

Answer 2

$left { {{x-y=2,} atop {x^3-y^3=56;}} right. left { {{x=y+2,} atop {(y+2)^3-y^3=56;}} right. \ y^3+6y^2+12y+8-y^3-56=0, \ 6y^2+12y-48=0, \ y^2+2y-8=0, \ y_1=-4, y_2=2; \ x_1=-2, x_2=4. \ (-2;-4), (4;2).$