Question

Решите систему х-у=2 х^3-y^3=56

Answer 1

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

Answer 2

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